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Oblique Derivative Problems For Elliptic Equations In Conical Domains
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Book Synopsis Oblique Derivative Problems for Elliptic Equations in Conical Domains by : Mikhail Borsuk
Download or read book Oblique Derivative Problems for Elliptic Equations in Conical Domains written by Mikhail Borsuk and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of our book is the investigation of the behavior of strong and weak solutions to the regular oblique derivative problems for second order elliptic equations, linear and quasi-linear, in the neighborhood of the boundary singularities. The main goal is to establish the precise exponent of the solution decrease rate and under the best possible conditions. The question on the behavior of solutions of elliptic boundary value problems near boundary singularities is of great importance for its many applications, e.g., in hydrodynamics, aerodynamics, fracture mechanics, in the geodesy etc. Only few works are devoted to the regular oblique derivative problems for second order elliptic equations in non-smooth domains. All results are given with complete proofs. The monograph will be of interest to graduate students and specialists in elliptic boundary value problems and their applications.
Book Synopsis Oblique Derivative Problems for Elliptic Equations in Conical Domains by : Mikhail Borsuk
Download or read book Oblique Derivative Problems for Elliptic Equations in Conical Domains written by Mikhail Borsuk and published by Springer Nature. This book was released on 2023-05-31 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of our book is the investigation of the behavior of strong and weak solutions to the regular oblique derivative problems for second order elliptic equations, linear and quasi-linear, in the neighborhood of the boundary singularities. The main goal is to establish the precise exponent of the solution decrease rate and under the best possible conditions. The question on the behavior of solutions of elliptic boundary value problems near boundary singularities is of great importance for its many applications, e.g., in hydrodynamics, aerodynamics, fracture mechanics, in the geodesy etc. Only few works are devoted to the regular oblique derivative problems for second order elliptic equations in non-smooth domains. All results are given with complete proofs. The monograph will be of interest to graduate students and specialists in elliptic boundary value problems and their applications.
Book Synopsis Interface Problems for Elliptic Second-Order Equations in Non-Smooth Domains by : Mikhail Borsuk
Download or read book Interface Problems for Elliptic Second-Order Equations in Non-Smooth Domains written by Mikhail Borsuk and published by Birkhäuser. This book was released on 2024-09-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to investigate the behavior of weak solutions to the elliptic interface problem in a neighborhood of boundary singularities: angular and conic points or edges. This problem is considered both for linear and quasi-linear equations, which are among the less studied varieties. As a second edition of Transmission Problems for Elliptic Second-Order Equations for Non-Smooth Domains (Birkhäuser, 2010), this volume includes two entirely new chapters: one about the oblique derivative problems for the perturbed p(x)-Laplacian equation in a bounded n-dimensional cone, and another about the existence of bounded weak solutions. Researchers and advanced graduate students will appreciate this compact compilation of new material in the field.
Book Synopsis Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains by : Mikhail Borsuk
Download or read book Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains written by Mikhail Borsuk and published by Springer Science & Business Media. This book was released on 2010-09-02 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the behaviour of weak solutions to the elliptic transmisssion problem in a neighborhood of boundary singularities: angular and conic points or edges, considering this problem both for linear and quasi-linear equations.
Book Synopsis Nonlinear Elliptic and Parabolic Problems by : Michel Chipot
Download or read book Nonlinear Elliptic and Parabolic Problems written by Michel Chipot and published by Springer Science & Business Media. This book was released on 2006-02-09 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celebrates the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Containing 32 contributions, this volume covers a range of nonlinear elliptic and parabolic equations, with applications to natural sciences and engineering.
Book Synopsis Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations by : Vladimir Kozlov
Download or read book Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations written by Vladimir Kozlov and published by American Mathematical Soc.. This book was released on 2001 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the analysis of eigenvalues and eigenfunctions that describe singularities of solutions to elliptic boundary value problems in domains with corners and edges. The authors treat both classical problems of mathematical physics and general elliptic boundary value problems. The volume is divided into two parts: The first is devoted to the power-logarithmic singularities of solutions to classical boundary value problems of mathematical physics. The second deals with similar singularities for higher order elliptic equations and systems. Chapter 1 collects basic facts concerning operator pencils acting in a pair of Hilbert spaces. Related properties of ordinary differential equations with constant operator coefficients are discussed and connections with the theory of general elliptic boundary value problems in domains with conic vertices are outlined. New results are presented. Chapter 2 treats the Laplace operator as a starting point and a model for the subsequent study of angular and conic singularities of solutions. Chapter 3 considers the Dirichlet boundary condition beginning with the plane case and turning to the space problems. Chapter 4 investigates some mixed boundary conditions. The Stokes system is discussed in Chapters 5 and 6, and Chapter 7 concludes with the Dirichlet problem for the polyharmonic operator. Chapter 8 studies the Dirichlet problem for general elliptic differential equations of order 2m in an angle. In Chapter 9, an asymptotic formula for the distribution of eigenvalues of operator pencils corresponding to general elliptic boundary value problems in an angle is obtained. Chapters 10 and 11 discuss the Dirichlet problem for elliptic systems of differential equations of order 2 in an n-dimensional cone. Chapter 12 studies the Neumann problem for general elliptic systems, in particular with eigenvalues of the corresponding operator pencil in the strip $\mid {\Re} \lambda - m + /2n \mid \leq 1/2$. It is shown that only integer numbers contained in this strip are eigenvalues. Applications are placed within chapter introductions and as special sections at the end of chapters. Prerequisites include standard PDE and functional analysis courses.
Book Synopsis Oblique Derivative Problems for Elliptic Equations by : Gary M. Lieberman
Download or read book Oblique Derivative Problems for Elliptic Equations written by Gary M. Lieberman and published by World Scientific. This book was released on 2013 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an up-to-date exposition on the theory of oblique derivative problems for elliptic equations. The modern analysis of shock reflection was made possible by the theory of oblique derivative problems developed by the author. Such problems also arise in many other physical situations such as the shape of a capillary surface and problems of optimal transportation. The author begins the book with basic results for linear oblique derivative problems and work through the theory for quasilinear and nonlinear problems. The final chapter discusses some of the applications. In addition, notes to each chapter give a history of the topics in that chapter and suggestions for further reading.
Book Synopsis Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains by : Mikhail S. Agranovich
Download or read book Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains written by Mikhail S. Agranovich and published by Springer. This book was released on 2015-05-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems. The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory and pseudodifferential operators, has included his own very recent findings in the present book. The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date. Graduate and post-graduate students, as well as specialists working in the fields of partial differential equations, functional analysis, operator theory and mathematical physics will find this book particularly valuable.
Book Synopsis Elliptic Equations in Polyhedral Domains by : V. G. Maz_i_a
Download or read book Elliptic Equations in Polyhedral Domains written by V. G. Maz_i_a and published by American Mathematical Soc.. This book was released on 2010-04-22 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph which systematically treats elliptic boundary value problems in domains of polyhedral type. The authors mainly describe their own recent results focusing on the Dirichlet problem for linear strongly elliptic systems of arbitrary order, Neumann and mixed boundary value problems for second order systems, and on boundary value problems for the stationary Stokes and Navier-Stokes systems. A feature of the book is the systematic use of Green's matrices. Using estimates for the elements of these matrices, the authors obtain solvability and regularity theorems for the solutions in weighted and non-weighted Sobolev and Holder spaces. Some classical problems of mathematical physics (Laplace and biharmonic equations, Lame system) are considered as examples. Furthermore, the book contains maximum modulus estimates for the solutions and their derivatives. The exposition is self-contained, and an introductory chapter provides background material on the theory of elliptic boundary value problems in domains with smooth boundaries and in domains with conical points. The book is destined for graduate students and researchers working in elliptic partial differential equations and applications.
Book Synopsis Current Trends in Analysis and Its Applications by : Vladimir V. Mityushev
Download or read book Current Trends in Analysis and Its Applications written by Vladimir V. Mityushev and published by Birkhäuser. This book was released on 2015-02-04 with total page 842 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers from the 9th International ISAAC Congress held in 2013 in Kraków, Poland. The papers are devoted to recent results in mathematics, focused on analysis and a wide range of its applications. These include up-to-date findings of the following topics: - Differential Equations: Complex and Functional Analytic Methods - Nonlinear PDE - Qualitative Properties of Evolution Models - Differential and Difference Equations - Toeplitz Operators - Wavelet Theory - Topological and Geometrical Methods of Analysis - Queueing Theory and Performance Evaluation of Computer Networks - Clifford and Quaternion Analysis - Fixed Point Theory - M-Frame Constructions - Spaces of Differentiable Functions of Several Real Variables Generalized Functions - Analytic Methods in Complex Geometry - Topological and Geometrical Methods of Analysis - Integral Transforms and Reproducing Kernels - Didactical Approaches to Mathematical Thinking Their wide applications in biomathematics, mechanics, queueing models, scattering, geomechanics etc. are presented in a concise, but comprehensible way, such that further ramifications and future directions can be immediately seen.
Book Synopsis Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains by : Michail Borsuk
Download or read book Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains written by Michail Borsuk and published by Elsevier. This book was released on 2006-01-12 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points. Key features: * New the Hardy – Friedrichs – Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m – Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration. * Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.
Book Synopsis Elliptic Problems in Domains with Piecewise Smooth Boundaries by : Sergey Nazarov
Download or read book Elliptic Problems in Domains with Piecewise Smooth Boundaries written by Sergey Nazarov and published by Walter de Gruyter. This book was released on 2011-06-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
Book Synopsis Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems by : Carlos E. Kenig
Download or read book Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems written by Carlos E. Kenig and published by American Mathematical Soc.. This book was released on 1994 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, there has been a great deal of activity in the study of boundary value problems with minimal smoothness assumptions on the coefficients or on the boundary of the domain in question. These problems are of interest both because of their theoretical importance and the implications for applications, and they have turned out to have profound and fascinating connections with many areas of analysis. Techniques from harmonic analysis have proved to be extremely useful in these studies, both as concrete tools in establishing theorems and as models which suggest what kind of result might be true. Kenig describes these developments and connections for the study of classical boundary value problems on Lipschitz domains and for the corresponding problems for second order elliptic equations in divergence form. He also points out many interesting problems in this area which remain open.
Book Synopsis Variational Analysis and Applications by : Franco Giannessi
Download or read book Variational Analysis and Applications written by Franco Giannessi and published by Springer Science & Business Media. This book was released on 2007-03-06 with total page 1163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Volume contains the (refereed) papers presented at the 38th Conference of the School of Mathematics "G.Stampacchia" of the "E.Majorana" Centre for Scientific Culture of Erice (Sicily), held in Memory ofG. Stampacchia and J.-L. Lions in the period June 20 - July 2003. The presence of participants from Countries has greatly contributed to the success of the meeting. The School of Mathematics was dedicated to Stampacchia, not only for his great mathematical achievements, but also because He founded it. The core of the Conference has been the various features of the Variational Analysis and their motivations and applications to concrete problems. Variational Analysis encompasses a large area of modem Mathematics, such as the classical Calculus of Variations, the theories of perturbation, approximation, subgradient, subderivates, set convergence and Variational Inequalities, and all these topics have been deeply and intensely dealt during the Conference. In particular, Variational Inequalities, which have been initiated by Stampacchia, inspired by Signorini Problem and the related work of G. Fichera, have offered a very great possibility of applications to several fundamental problems of Mathematical Physics, Engineering, Statistics and Economics. The pioneer work of Stampacchia and Lions can be considered as the basic kernel around which Variational Analysis is going to be outlined and constructed. The Conference has dealt with both finite and infinite dimensional analysis, showing that to carry on these two aspects disjointly is unsuitable for both.
Book Synopsis Partial Differential Equations IX by : M.S. Agranovich
Download or read book Partial Differential Equations IX written by M.S. Agranovich and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This EMS volume gives an overview of the modern theory of elliptic boundary value problems, with contributions focusing on differential elliptic boundary problems and their spectral properties, elliptic pseudodifferential operators, and general differential elliptic boundary value problems in domains with singularities.
Book Synopsis New Directions in Mathematical Fluid Mechanics by : Andrei V. Fursikov
Download or read book New Directions in Mathematical Fluid Mechanics written by Andrei V. Fursikov and published by Springer Science & Business Media. This book was released on 2010-01-11 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: On November 3, 2005, Alexander Vasil’evich Kazhikhov left this world, untimely and unexpectedly. He was one of the most in?uential mathematicians in the mechanics of ?uids, and will be remembered for his outstanding results that had, and still have, a c- siderablysigni?cantin?uenceinthe?eld.Amonghis manyachievements,werecall that he was the founder of the modern mathematical theory of the Navier-Stokes equations describing one- and two-dimensional motions of a viscous, compressible and heat-conducting gas. A brief account of Professor Kazhikhov’s contributions to science is provided in the following article “Scienti?c portrait of Alexander Vasil’evich Kazhikhov”. This volume is meant to be an expression of high regard to his memory, from most of his friends and his colleagues. In particular, it collects a selection of papers that represent the latest progress in a number of new important directions of Mathematical Physics, mainly of Mathematical Fluid Mechanics. These papers are written by world renowned specialists. Most of them were friends, students or colleagues of Professor Kazhikhov, who either worked with him directly, or met him many times in o?cial scienti?c meetings, where they had the opportunity of discussing problems of common interest.
Book Synopsis Partial Differential Equations by : M. S. Agranovich
Download or read book Partial Differential Equations written by M. S. Agranovich and published by American Mathematical Soc.. This book was released on 2002 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplecticgeometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and general unbounded domains, linear elliptic problems with a parameter for mixed order systems, infinite-dimensional Schrodinger equations, Navier-Stokes equations, and nonlinear Maxwellequations. The book ends on a historical note with a paper about Vishik's seminar as a whole and a list of selected talks given from 1964 through 1989. The book is suitable for graduate students and researchers in pure and applied mathematics and mathematical physics.
