Regularity Of Free Boundaries In Obstacle Type Problems

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Regularity of Free Boundaries in Obstacle-type Problems

Author : Arshak Petrosyan
Publisher : American Mathematical Soc.
ISBN 13 : 0821887947
Total Pages : 221 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Regularity of Free Boundaries in Obstacle-type Problems by : Arshak Petrosyan

Download or read book Regularity of Free Boundaries in Obstacle-type Problems written by Arshak Petrosyan and published by American Mathematical Soc.. This book was released on 2012 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: The regularity theory of free boundaries flourished during the late 1970s and early 1980s and had a major impact in several areas of mathematics, mathematical physics, and industrial mathematics, as well as in applications. Since then the theory continued to evolve. Numerous new ideas, techniques, and methods have been developed, and challenging new problems in applications have arisen. The main intention of the authors of this book is to give a coherent introduction to the study of the regularity properties of free boundaries for a particular type of problems, known as obstacle-type problems. The emphasis is on the methods developed in the past two decades. The topics include optimal regularity, nondegeneracy, rescalings and blowups, classification of global solutions, several types of monotonicity formulas, Lipschitz, $C^1$, as well as higher regularity of the free boundary, structure of the singular set, touch of the free and fixed boundaries, and more. The book is based on lecture notes for the courses and mini-courses given by the authors at various locations and should be accessible to advanced graduate students and researchers in analysis and partial differential equations.

The obstacle problem

Author : Luis Angel Caffarelli
Publisher : Edizioni della Normale
ISBN 13 : 9788876422492
Total Pages : 0 pages
Book Rating : 4.4/5 (224 download)

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Book Synopsis The obstacle problem by : Luis Angel Caffarelli

Download or read book The obstacle problem written by Luis Angel Caffarelli and published by Edizioni della Normale. This book was released on 1999-10-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material presented here corresponds to Fermi lectures that I was invited to deliver at the Scuola Normale di Pisa in the spring of 1998. The obstacle problem consists in studying the properties of minimizers of the Dirichlet integral in a domain D of Rn, among all those configurations u with prescribed boundary values and costrained to remain in D above a prescribed obstacle F. In the Hilbert space H1(D) of all those functions with square integrable gradient, we consider the closed convex set K of functions u with fixed boundary value and which are greater than F in D. There is a unique point in K minimizing the Dirichlet integral. That is called the solution to the obstacle problem.

Free Boundary Problems

Author : Darya Apushkinskaya
Publisher : Springer
ISBN 13 : 3319970798
Total Pages : 146 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Free Boundary Problems by : Darya Apushkinskaya

Download or read book Free Boundary Problems written by Darya Apushkinskaya and published by Springer. This book was released on 2018-09-20 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with several elliptic and parabolic obstacle-type problems with a focus on the cases where the free and fixed boundaries meet. The results presented complement those found in existing books in the subject, which mainly treat regularity properties away from the fixed boundary. The topics include optimal regularity, analysis of global solutions, tangential touch of the free and fixed boundaries, as well as Lipschitz- and $C^1$-regularity of the free boundary. Special attention is given to local versions of various monotonicity formulas. The intended audience includes research mathematicians and advanced graduate students interested in problems with free boundaries.

Regularity of Free Boundaries in Obstacle-type Problems

Author : Arshak Petrosyan
Publisher : American Mathematical Soc.
ISBN 13 : 0821889923
Total Pages : 233 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Regularity of Free Boundaries in Obstacle-type Problems by : Arshak Petrosyan

Geometric Measure Theory and Free Boundary Problems

Author : Guido De Philippis
Publisher : Springer Nature
ISBN 13 : 303065799X
Total Pages : 138 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Geometric Measure Theory and Free Boundary Problems by : Guido De Philippis

Download or read book Geometric Measure Theory and Free Boundary Problems written by Guido De Philippis and published by Springer Nature. This book was released on 2021-03-23 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school “Geometric Measure Theory and Applications – From Geometric Analysis to Free Boundary Problems” which took place in Cetraro, Italy, under the scientific direction of Matteo Focardi and Emanuele Spadaro. Providing a description of the structure of measures satisfying certain differential constraints, and covering regularity theory for Bernoulli type free boundary problems and water waves as well as regularity theory for the obstacle problems and the developments leading to applications to the Stefan problem, this volume will be of interest to students and researchers in mathematical analysis and its applications.

Obstacle Problems in Mathematical Physics

Author : J.-F. Rodrigues
Publisher : Elsevier
ISBN 13 : 9780080872452
Total Pages : 351 pages
Book Rating : 4.8/5 (724 download)

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Book Synopsis Obstacle Problems in Mathematical Physics by : J.-F. Rodrigues

Download or read book Obstacle Problems in Mathematical Physics written by J.-F. Rodrigues and published by Elsevier. This book was released on 1987-03-01 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics. The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitation problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile.

A Geometric Approach to Free Boundary Problems

Author : Luis A. Caffarelli
Publisher : American Mathematical Soc.
ISBN 13 : 0821837842
Total Pages : 282 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Geometric Approach to Free Boundary Problems by : Luis A. Caffarelli

Download or read book A Geometric Approach to Free Boundary Problems written by Luis A. Caffarelli and published by American Mathematical Soc.. This book was released on 2005 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: We hope that the tools and ideas presented here will serve as a basis for the study of more complex phenomena and problems."--Jacket.

The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures

$Download The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures PDF Online Free$

Author : Gui-Qiang G Chen
Publisher : Princeton University Press
ISBN 13 : 0691160554
Total Pages : 829 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures by : Gui-Qiang G Chen

Download or read book The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures written by Gui-Qiang G Chen and published by Princeton University Press. This book was released on 2018-02-27 with total page 829 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development. Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws—PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs—mixed type, free boundaries, and corner singularities—that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities.

Geometry of PDEs and Related Problems

Author : Xavier Cabré
Publisher : Springer
ISBN 13 : 3319951866
Total Pages : 198 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Geometry of PDEs and Related Problems by : Xavier Cabré

Download or read book Geometry of PDEs and Related Problems written by Xavier Cabré and published by Springer. This book was released on 2018-10-03 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present different aspects of the deep interplay between Partial Differential Equations and Geometry. It gives an overview of some of the themes of recent research in the field and their mutual links, describing the main underlying ideas, and providing up-to-date references. Collecting together the lecture notes of the five mini-courses given at the CIME Summer School held in Cetraro (Cosenza, Italy) in the week of June 19–23, 2017, the volume presents a friendly introduction to a broad spectrum of up-to-date and hot topics in the study of PDEs, describing the state-of-the-art in the subject. It also gives further details on the main ideas of the proofs, their technical difficulties, and their possible extension to other contexts. Aiming to be a primary source for researchers in the field, the book will attract potential readers from several areas of mathematics.

Mathematics and Computation

Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem

Author : Donatella Daniell
Publisher : American Mathematical Soc.
ISBN 13 : 1470425475
Total Pages : 103 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem by : Donatella Daniell

Download or read book Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem written by Donatella Daniell and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a comprehensive treatment of the parabolic Signorini problem based on a generalization of Almgren's monotonicity of the frequency. This includes the proof of the optimal regularity of solutions, classification of free boundary points, the regularity of the regular set and the structure of the singular set.

Almgren's Big Regularity Paper

Author : Frederick J. Almgren
Publisher : World Scientific
ISBN 13 : 9789810241087
Total Pages : 976 pages
Book Rating : 4.2/5 (41 download)

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Book Synopsis Almgren's Big Regularity Paper by : Frederick J. Almgren

Download or read book Almgren's Big Regularity Paper written by Frederick J. Almgren and published by World Scientific. This book was released on 2000 with total page 976 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fred Almgren created the excess method for proving regularity theorems in the calculus of variations. His techniques yielded Holder continuity except for a small closed singular set. In the sixties and seventies Almgren refined and generalized his methods. Between 1974 and 1984 he wrote a 1,700-page proof that was his most ambitious exposition of his ground-breaking ideas. Originally, this monograph was available only as a three-volume work of limited circulation. The entire text is faithfully reproduced here. This book gives a complete proof of the interior regularity of an area-minimizing rectifiable current up to Hausdorff codimension 2. The argument uses the theory of Q-valued functions, which is developed in detail. For example, this work shows how first variation estimates from squash and squeeze deformations yield a monotonicity theorem for the normalized frequency of oscillation of a Q-valued function that minimizes a generalized Dirichlet integral. The principal features of the book include an extension theorem analogous to Kirszbraun's theorem and theorems on the approximation in mass of nearly flat mass-minimizing rectifiable currents by graphs and images of Lipschitz Q-valued functions.

Kernel Functions and Elliptic Differential Equations in Mathematical Physics

Author : Stefan Bergman
Publisher : Courier Corporation
ISBN 13 : 0486154653
Total Pages : 450 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Kernel Functions and Elliptic Differential Equations in Mathematical Physics by : Stefan Bergman

Download or read book Kernel Functions and Elliptic Differential Equations in Mathematical Physics written by Stefan Bergman and published by Courier Corporation. This book was released on 2013-01-23 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the theory of boundary value problems in partial differential equations and discusses a portion of the theory from a unifying point of view while providing an introduction to each branch of its applications. 1953 edition.

The Monge—Ampère Equation

Author : Cristian E. Gutierrez
Publisher : Springer Science & Business Media
ISBN 13 : 9780817641771
Total Pages : 148 pages
Book Rating : 4.6/5 (417 download)

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Book Synopsis The Monge—Ampère Equation by : Cristian E. Gutierrez

Download or read book The Monge—Ampère Equation written by Cristian E. Gutierrez and published by Springer Science & Business Media. This book was released on 2001-05-11 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Monge-Ampère equation has attracted considerable interest in recent years because of its important role in several areas of applied mathematics. Monge-Ampère type equations have applications in the areas of differential geometry, the calculus of variations, and several optimization problems, such as the Monge-Kantorovitch mass transfer problem. This book stresses the geometric aspects of this beautiful theory, using techniques from harmonic analysis – covering lemmas and set decompositions.

Optimal Shape Design

Author : B. Kawohl
Publisher : Springer Science & Business Media
ISBN 13 : 9783540679714
Total Pages : 404 pages
Book Rating : 4.6/5 (797 download)

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Book Synopsis Optimal Shape Design by : B. Kawohl

Download or read book Optimal Shape Design written by B. Kawohl and published by Springer Science & Business Media. This book was released on 2000-11-16 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal Shape Design is concerned with the optimization of some performance criterion dependent (besides the constraints of the problem) on the "shape" of some region. The main topics covered are: the optimal design of a geometrical object, for instance a wing, moving in a fluid; the optimal shape of a region (a harbor), given suitable constraints on the size of the entrance to the harbor, subject to incoming waves; the optimal design of some electrical device subject to constraints on the performance. The aim is to show that Optimal Shape Design, besides its interesting industrial applications, possesses nontrivial mathematical aspects. The main theoretical tools developed here are the homogenization method and domain variations in PDE. The style is mathematically rigorous, but specifically oriented towards applications, and it is intended for both pure and applied mathematicians. The reader is required to know classical PDE theory and basic functional analysis.

Introduction to Numerical Methods for Variational Problems

Author : Hans Petter Langtangen
Publisher : Springer Nature
ISBN 13 : 3030237885
Total Pages : 395 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Introduction to Numerical Methods for Variational Problems by : Hans Petter Langtangen

Download or read book Introduction to Numerical Methods for Variational Problems written by Hans Petter Langtangen and published by Springer Nature. This book was released on 2019-09-26 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.

Free Boundary Problems

Author : Ioannis Athanasopoulos
Publisher : Routledge
ISBN 13 : 1351447149
Total Pages : 366 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Free Boundary Problems by : Ioannis Athanasopoulos

Download or read book Free Boundary Problems written by Ioannis Athanasopoulos and published by Routledge. This book was released on 2019-11-11 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Free boundary problems arise in an enormous number of situations in nature and technology. They hold a strategic position in pure and applied sciences and thus have been the focus of considerable research over the last three decades. Free Boundary Problems: Theory and Applications presents the work and results of experts at the forefront of current research in mathematics, material sciences, chemical engineering, biology, and physics. It contains the plenary lectures and contributed papers of the 1997 International Interdisciplinary Congress proceedings held in Crete. The main topics addressed include free boundary problems in fluid and solid mechanics, combustion, the theory of filtration, and glaciology. Contributors also discuss material science modeling, recent mathematical developments, and numerical analysis advances within their presentations of more specific topics, such as singularities of interfaces, cusp cavitation and fracture, capillary fluid dynamics of film coating, dynamics of surface growth, phase transition kinetics, and phase field models. With the implications of free boundary problems so far reaching, it becomes important for researchers from all of these fields to stay abreast of new developments. Free Boundary Problems: Theory and Applications provides the opportunity to do just that, presenting recent advances from more than 50 researchers at the frontiers of science, mathematics, and technology.