Existence And Regularity Results For Some Shape Optimization Problems

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Existence and Regularity Results for Some Shape Optimization Problems

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Author : Bozhidar Velichkov
Publisher : Springer
ISBN 13 : 8876425276
Total Pages : 362 pages
Book Rating : 4.8/5 (764 download)

Book Synopsis Existence and Regularity Results for Some Shape Optimization Problems by : Bozhidar Velichkov

Download or read book Existence and Regularity Results for Some Shape Optimization Problems written by Bozhidar Velichkov and published by Springer. This book was released on 2015-03-21 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the existence and regularity of optimal domains for functionals depending on the spectrum of the Dirichlet Laplacian or of more general Schrödinger operators. The domains are subject to perimeter and volume constraints; we also take into account the possible presence of geometric obstacles. We investigate the properties of the optimal sets and of the optimal state functions. In particular, we prove that the eigenfunctions are Lipschitz continuous up to the boundary and that the optimal sets subject to the perimeter constraint have regular free boundary. We also consider spectral optimization problems in non-Euclidean settings and optimization problems for potentials and measures, as well as multiphase and optimal partition problems.

New Trends in Shape Optimization

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Author : Aldo Pratelli
Publisher : Birkhäuser
ISBN 13 : 3319175637
Total Pages : 312 pages
Book Rating : 4.3/5 (191 download)

Book Synopsis New Trends in Shape Optimization by : Aldo Pratelli

Download or read book New Trends in Shape Optimization written by Aldo Pratelli and published by Birkhäuser. This book was released on 2015-12-01 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects “New Trends in Shape Optimization” and is based on a workshop of the same name organized at the Friedrich-Alexander University Erlangen-Nürnberg in September 2013. During the workshop senior mathematicians and young scientists alike presented their latest findings. The format of the meeting allowed fruitful discussions on challenging open problems, and triggered a number of new and spontaneous collaborations. As such, the idea was born to produce this book, each chapter of which was written by a workshop participant, often with a collaborator. The content of the individual chapters ranges from survey papers to original articles; some focus on the topics discussed at the Workshop, while others involve arguments outside its scope but which are no less relevant for the field today. As such, the book offers readers a balanced introduction to the emerging field of shape optimization.

Regularity of the One-phase Free Boundaries

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Author : Bozhidar Velichkov
Publisher : Springer Nature
ISBN 13 : 3031132386
Total Pages : 249 pages
Book Rating : 4.0/5 (311 download)

Book Synopsis Regularity of the One-phase Free Boundaries by : Bozhidar Velichkov

Download or read book Regularity of the One-phase Free Boundaries written by Bozhidar Velichkov and published by Springer Nature. This book was released on 2023-02-24 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book is an introduction to the regularity theory for free boundary problems. The focus is on the one-phase Bernoulli problem, which is of particular interest as it deeply influenced the development of the modern free boundary regularity theory and is still an object of intensive research. The exposition is organized around four main theorems, which are dedicated to the one-phase functional in its simplest form. Many of the methods and the techniques presented here are very recent and were developed in the context of different free boundary problems. We also give the detailed proofs of several classical results, which are based on some universal ideas and are recurrent in the free boundary, PDE and the geometric regularity theories. This book is aimed at graduate students and researches and is accessible to anyone with a moderate level of knowledge of elliptical PDEs.

Non-Smooth and Complementarity-Based Distributed Parameter Systems

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Author : Michael Hintermüller
Publisher : Springer Nature
ISBN 13 : 3030793931
Total Pages : 518 pages
Book Rating : 4.0/5 (37 download)

Book Synopsis Non-Smooth and Complementarity-Based Distributed Parameter Systems by : Michael Hintermüller

Download or read book Non-Smooth and Complementarity-Based Distributed Parameter Systems written by Michael Hintermüller and published by Springer Nature. This book was released on 2022-02-18 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks. Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.

Recent Advances in Partial Differential Equations and Applications

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Author : Vicenţiu D. Rădulescu
Publisher : American Mathematical Soc.
ISBN 13 : 1470415216
Total Pages : 418 pages
Book Rating : 4.4/5 (74 download)

Book Synopsis Recent Advances in Partial Differential Equations and Applications by : Vicenţiu D. Rădulescu

Download or read book Recent Advances in Partial Differential Equations and Applications written by Vicenţiu D. Rădulescu and published by American Mathematical Soc.. This book was released on 2016-06-28 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Conference on Recent Advances in PDEs and Applications, in honor of Hugo Beirão da Veiga's 70th birthday, held from February 17–21, 2014, in Levico Terme, Italy. The conference brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants. The workshop program testified to the wide-ranging influence of Hugo Beirão da Veiga on the field of partial differential equations, in particular those related to fluid dynamics. In his own work, da Veiga has been a seminal influence in many important areas: Navier-Stokes equations, Stokes systems, non-Newtonian fluids, Euler equations, regularity of solutions, perturbation theory, vorticity phenomena, and nonlinear potential theory, as well as various degenerate or singular models in mathematical physics. This same breadth is reflected in the mathematical papers included in this volume.

Shape Optimization Problems

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Author : Hideyuki Azegami
Publisher : Springer Nature
ISBN 13 : 9811576181
Total Pages : 646 pages
Book Rating : 4.8/5 (115 download)

Book Synopsis Shape Optimization Problems by : Hideyuki Azegami

Download or read book Shape Optimization Problems written by Hideyuki Azegami and published by Springer Nature. This book was released on 2020-09-30 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background. Non-parametric shape optimization problems are defined as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. In these problems, optimum shapes are obtained from an arbitrary form without any geometrical parameters previously assigned. In particular, problems in which the optimum shape is sought by making a hole in domain are called topology optimization problems. Moreover, a problem in which the optimum shape is obtained based on domain variation is referred to as a shape optimization problem of domain variation type, or a shape optimization problem in a limited sense. Software has been developed to solve these problems, and it is being used to seek practical optimum shapes. However, there are no books explaining such theories beginning with their foundations. The structure of the book is shown in the Preface. The theorems are built up using mathematical results. Therefore, a mathematical style is introduced, consisting of definitions and theorems to summarize the key points. This method of expression is advanced as provable facts are clearly shown. If something to be investigated is contained in the framework of mathematics, setting up a theory using theorems prepared by great mathematicians is thought to be an extremely effective approach. However, mathematics attempts to heighten the level of abstraction in order to understand many things in a unified fashion. This characteristic may baffle readers with an engineering background. Hence in this book, an attempt has been made to provide explanations in engineering terms, with examples from mechanics, after accurately denoting the provable facts using definitions and theorems.

Variational Methods in Shape Optimization Problems

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Author : Dorin Bucur
Publisher : Springer Science & Business Media
ISBN 13 : 0817644032
Total Pages : 218 pages
Book Rating : 4.8/5 (176 download)

Book Synopsis Variational Methods in Shape Optimization Problems by : Dorin Bucur

Download or read book Variational Methods in Shape Optimization Problems written by Dorin Bucur and published by Springer Science & Business Media. This book was released on 2006-09-13 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.

Shape Optimization and Spectral Theory

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Author : Antoine Henrot
Publisher : De Gruyter Open
ISBN 13 : 9783110550856
Total Pages : 474 pages
Book Rating : 4.5/5 (58 download)

Book Synopsis Shape Optimization and Spectral Theory by : Antoine Henrot

Download or read book Shape Optimization and Spectral Theory written by Antoine Henrot and published by De Gruyter Open. This book was released on 2017-05-08 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Shape optimization and spectral theory" is a survey book aiming to give an overview of recent results in spectral geometry and its links with shape optimization. It covers most of the issues which are important for people working in PDE and differential geometry interested in sharp inequalities and qualitative behaviour for eigenvalues of the Laplacian with different kind of boundary conditions (Dirichlet, Robin and Steklov). This includes: existence of optimal shapes, their regularity, the case of special domains like triangles, isospectrality, quantitative form of the isoperimetric inequalities, optimal partitions, universal inequalities and numerical results. Much progress has been made in these extremum problems during the last ten years and this edited volume presents a valuable update to a wide community interested in these topics. List of contributors Antunes Pedro R.S., Ashbaugh Mark, Bonnaillie-Noel Virginie, Brasco Lorenzo, Bucur Dorin, Buttazzo Giuseppe, De Philippis Guido, Freitas Pedro, Girouard Alexandre, Helffer Bernard, Kennedy James, Lamboley Jimmy, Laugesen Richard S., Oudet Edouard, Pierre Michel, Polterovich Iosif, Siudeja Bartlomiej A., Velichkov Bozhidar

Variational methods in some shape optimization problems

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Author : Dorin Bucur
Publisher : Edizioni della Normale
ISBN 13 : 9788876422973
Total Pages : 217 pages
Book Rating : 4.4/5 (229 download)

Book Synopsis Variational methods in some shape optimization problems by : Dorin Bucur

Download or read book Variational methods in some shape optimization problems written by Dorin Bucur and published by Edizioni della Normale. This book was released on 2002-10-01 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of shape optimization problems is a very wide field, both classical, as the isoperimetric problem and Newton problem of the best aerodynamical shape show, and modern, for all the recent results obtained in the last two, three decades. The fascinating feature is that the competing objects are shapes, i.e. domains of Rn, instead of functions, as usually occurs in problems of calculus of variations. This constraint often produces additional difficulties that lead to a lack of existence of a solution and the introduction of suitable relaxed formulations of the problem. However, in a few cases an optimal solution exists, due to the special form of the cost functional and to the geometrical restriction on the class of competing domains. This volume collects the lecture notes of two courses given in the academic year 2000/01 by the authors at the University of Pisa and at the Scuola Normale Superiore respectively. The courses were mainly addressed to Ph. D. students and required a background in the topics in functional analysis that are usually taught in undergraduate courses.

Trends in PDE Constrained Optimization

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Author : Günter Leugering
Publisher : Springer
ISBN 13 : 3319050834
Total Pages : 539 pages
Book Rating : 4.3/5 (19 download)

Book Synopsis Trends in PDE Constrained Optimization by : Günter Leugering

Download or read book Trends in PDE Constrained Optimization written by Günter Leugering and published by Springer. This book was released on 2014-12-22 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of research was studied and further explored as part of the Deutsche Forschungsgemeinschaft (DFG) priority program 1253 on “Optimization with Partial Differential Equations” from 2006 to 2013. The investigations were motivated by the fascinating potential applications and challenging mathematical problems that arise in the field of PDE constrained optimization. New analytic and algorithmic paradigms have been developed, implemented and validated in the context of real-world applications. In this special volume, contributions from more than fifteen German universities combine the results of this interdisciplinary program with a focus on applied mathematics. The book is divided into five sections on “Constrained Optimization, Identification and Control”, “Shape and Topology Optimization”, “Adaptivity and Model Reduction”, “Discretization: Concepts and Analysis” and “Applications”. Peer-reviewed research articles present the most recent results in the field of PDE constrained optimization and control problems. Informative survey articles give an overview of topics that set sustainable trends for future research. This makes this special volume interesting not only for mathematicians, but also for engineers and for natural and medical scientists working on processes that can be modeled by PDEs.

Partial Differential Equations On Multistructures

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Author : Felix Mehmeti
Publisher : CRC Press
ISBN 13 : 0824745043
Total Pages : 288 pages
Book Rating : 4.8/5 (247 download)

Book Synopsis Partial Differential Equations On Multistructures by : Felix Mehmeti

Download or read book Partial Differential Equations On Multistructures written by Felix Mehmeti and published by CRC Press. This book was released on 2001-04-10 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is based on lectures presented at the International Conference on Partial Differential Equations (PDEs) on Multistructures, held in Luminy, France. It contains advances in the field, compiling research on the analyses and applications of multistructures - including treatments of classical theories, specific characterizations and modellings of multistructures, and discussions on uses in physics, electronics, and biology.

A Course in the Calculus of Variations

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Author : Filippo Santambrogio
Publisher : Springer Nature
ISBN 13 : 3031450361
Total Pages : 354 pages
Book Rating : 4.0/5 (314 download)

Book Synopsis A Course in the Calculus of Variations by : Filippo Santambrogio

Download or read book A Course in the Calculus of Variations written by Filippo Santambrogio and published by Springer Nature. This book was released on 2024-01-18 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present. Beginning with the scientific modeling that motivates the subject, the book then tackles mathematical questions such as the existence and uniqueness of solutions, their characterization in terms of partial differential equations, and their regularity. It includes both classical and recent results on one-dimensional variational problems, as well as the adaptation to the multi-dimensional case. Here, convexity plays an important role in establishing semi-continuity results and connections with techniques from optimization, and convex duality is even used to produce regularity results. This is then followed by the more classical Hölder regularity theory for elliptic PDEs and some geometric variational problems on sets, including the isoperimetric inequality and the Steiner tree problem. The book concludes with a chapter on the limits of sequences of variational problems, expressed in terms of Γ-convergence. While primarily designed for master's-level and advanced courses, this textbook, based on its author's instructional experience, also offers original insights that may be of interest to PhD students and researchers. A foundational understanding of measure theory and functional analysis is required, but all the essential concepts are reiterated throughout the book using special memo-boxes.

Existence for Shape Optimization Problems in Arbitrary Dimension

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Author : W. B. Liu
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (839 download)

Book Synopsis Existence for Shape Optimization Problems in Arbitrary Dimension by : W. B. Liu

Download or read book Existence for Shape Optimization Problems in Arbitrary Dimension written by W. B. Liu and published by . This book was released on 1999 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Optimal Control of Partial Differential Equations

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Author : Karl-Heinz Hoffmann
Publisher : Birkhäuser
ISBN 13 : 3034886918
Total Pages : 324 pages
Book Rating : 4.0/5 (348 download)

Book Synopsis Optimal Control of Partial Differential Equations by : Karl-Heinz Hoffmann

Download or read book Optimal Control of Partial Differential Equations written by Karl-Heinz Hoffmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application of PDE-based control theory and the corresponding numerical algorithms to industrial problems have become increasingly important in recent years. This volume offers a wide spectrum of aspects of the discipline, and is of interest to mathematicians and scientists working in the field.

Shape Optimization And Optimal Design

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Author : John Cagnol
Publisher : CRC Press
ISBN 13 : 9780203904169
Total Pages : 458 pages
Book Rating : 4.9/5 (41 download)

Book Synopsis Shape Optimization And Optimal Design by : John Cagnol

Download or read book Shape Optimization And Optimal Design written by John Cagnol and published by CRC Press. This book was released on 2017-08-02 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents developments and advances in modelling passive and active control systems governed by partial differential equations. It emphasizes shape analysis, optimal shape design, controllability, nonlinear boundary control, and stabilization. The authors include essential data on exact boundary controllability of thermoelastic plates with variable transmission coefficients.

Advances in Mathematical Sciences and Applications

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Author :
Publisher :
ISBN 13 :
Total Pages : 744 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis Advances in Mathematical Sciences and Applications by :

Download or read book Advances in Mathematical Sciences and Applications written by and published by . This book was released on 2004 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Reviews

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Author :
Publisher :
ISBN 13 :
Total Pages : 1164 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 1164 pages. Available in PDF, EPUB and Kindle. Book excerpt: