Elliptic Regularity Theory By Approximation Methods
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Elliptic Regularity Theory By Approximation Methods
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Author : Edgard A. Pimentel
language : en
Publisher: Cambridge University Press
Release Date : 2022-09-29
Elliptic Regularity Theory By Approximation Methods written by Edgard A. Pimentel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-29 with Mathematics categories.
A modern account of elliptic regularity theory, with a rigorous presentation of recent developments for fundamental models.
Elliptic Regularity Theory By Approximation Methods
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Author : Edgard A. Pimentel
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-30
Elliptic Regularity Theory By Approximation Methods written by Edgard A. Pimentel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-30 with Mathematics categories.
Presenting the basics of elliptic PDEs in connection with regularity theory, the book bridges fundamental breakthroughs – such as the Krylov–Safonov and Evans–Krylov results, Caffarelli's regularity theory, and the counterexamples due to Nadirashvili and Vlăduţ – and modern developments, including improved regularity for flat solutions and the partial regularity result. After presenting this general panorama, accounting for the subtleties surrounding C-viscosity and Lp-viscosity solutions, the book examines important models through approximation methods. The analysis continues with the asymptotic approach, based on the recession operator. After that, approximation techniques produce a regularity theory for the Isaacs equation, in Sobolev and Hölder spaces. Although the Isaacs operator lacks convexity, approximation methods are capable of producing Hölder continuity for the Hessian of the solutions by connecting the problem with a Bellman equation. To complete the book, degenerate models are studied and their optimal regularity is described.
Elliptic Regularity Theory
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Author : Lisa Beck
language : en
Publisher: Springer
Release Date : 2016-04-08
Elliptic Regularity Theory written by Lisa Beck and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-08 with Mathematics categories.
These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After a short review of some classical results on everywhere regularity for scalar-valued weak solutions, the presentation focuses on vector-valued weak solutions to a system of several coupled equations. In the vectorial case, weak solutions may have discontinuities and so are expected, in general, to be regular only outside of a set of measure zero. Several methods are presented concerning the proof of such partial regularity results, and optimal regularity is discussed. Finally, a short overview is given on the current state of the art concerning the size of the singular set on which discontinuities may occur. The notes are intended for graduate and postgraduate students with a solid background in functional analysis and some familiarity with partial differential equations; they will also be of interest to researchers working on related topics.
Numerical Solution Of Elliptic And Parabolic Partial Differential Equations
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Author : John Arthur Trangenstein
language : en
Publisher:
Release Date : 2013
Numerical Solution Of Elliptic And Parabolic Partial Differential Equations written by John Arthur Trangenstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
"For mathematicians and engineers interested in applying numerical methods to physical problems this book is ideal. Numerical ideas are connected to accompanying software, which is also available online. By seeing the complete description of the methods in both theory and implementation, students will more easily gain the knowledge needed to write their own application programs or develop new theory. The book contains careful development of the mathematical tools needed for analysis of the numerical methods, including elliptic regularity theory and approximation theory. Variational crimes, due to quadrature, coordinate mappings, domain approximation and boundary conditions, are analyzed. The claims are stated with full statement of the assumptions and conclusions, and use subscripted constants which can be traced back to the origination (particularly in the electronic version, which is available online and on the accompanying CD-ROM)"--
Numerical Solution Of Hyperbolic Partial Differential Equations
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Author : John A. Trangenstein
language : en
Publisher: Cambridge University Press
Release Date : 2009-09-03
Numerical Solution Of Hyperbolic Partial Differential Equations written by John A. Trangenstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-03 with Mathematics categories.
Numerical Solution of Hyperbolic Partial Differential Equations is a new type of graduate textbook, with both print and interactive electronic components (on CD). It is a comprehensive presentation of modern shock-capturing methods, including both finite volume and finite element methods, covering the theory of hyperbolic conservation laws and the theory of the numerical methods. The range of applications is broad enough to engage most engineering disciplines and many areas of applied mathematics. Classical techniques for judging the qualitative performance of the schemes are used to motivate the development of classical higher-order methods. The interactive CD gives access to the computer code used to create all of the text's figures, and lets readers run simulations, choosing their own input parameters; the CD displays the results of the experiments as movies. Consequently, students can gain an appreciation for both the dynamics of the problem application, and the growth of numerical errors.
The New Method Of Regularity Theory And Its Applications
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Author : Shuhong Chen
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2012
The New Method Of Regularity Theory And Its Applications written by Shuhong Chen and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Analytic functions categories.
Regularity theory is one of the most challenging problems in modern theory of partial differential equations. It has attracted peoples' eyes for a long history. A classical method of partial regularity theory is the "freezing the coefficients" method. The proof is complex and troublesome. And the result obtained by this method is not optimal. In this book, we use the method of A-harmonic approximation, to consider regularity theory for nonlinear partial differential systems. The new method not only allows one to simplify the procedure of proof, but also to establish optimal regularity results directly. This book should be useful to professionals in partial differential equations.
Numerical Solution Of Elliptic And Parabolic Partial Differential Equations With Cd Rom
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Author : John A. Trangenstein
language : en
Publisher: Cambridge University Press
Release Date : 2013-04-18
Numerical Solution Of Elliptic And Parabolic Partial Differential Equations With Cd Rom written by John A. Trangenstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
For mathematicians and engineers interested in applying numerical methods to physical problems this book is ideal. Numerical ideas are connected to accompanying software, which is also available online. By seeing the complete description of the methods in both theory and implementation, students will more easily gain the knowledge needed to write their own application programs or develop new theory. The book contains careful development of the mathematical tools needed for analysis of the numerical methods, including elliptic regularity theory and approximation theory. Variational crimes, due to quadrature, coordinate mappings, domain approximation and boundary conditions, are analyzed. The claims are stated with full statement of the assumptions and conclusions, and use subscripted constants which can be traced back to the origination (particularly in the electronic version, which can be found on the accompanying CD-ROM).
Introduction To Regularity Theory For Nonlinear Elliptic Systems
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Author : Mariano Giaquinta
language : en
Publisher: Birkhäuser
Release Date : 1993-06-01
Introduction To Regularity Theory For Nonlinear Elliptic Systems written by Mariano Giaquinta and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-06-01 with Mathematics categories.
These lectures are an introduction to the regularity theory of minimizers of variational integrals, in the calculus of variations and of solutions of nonlinear elliptic systems. Topics covered include the Hilbert-space approach to boundary value problems and energy estimates.
Numerical Methods For Nonlinear Elliptic Differential Equations
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Author : Klaus Böhmer
language : en
Publisher: Oxford University Press
Release Date : 2010-10-07
Numerical Methods For Nonlinear Elliptic Differential Equations written by Klaus Böhmer and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-07 with Computers categories.
Boehmer systmatically handles the different numerical methods for nonlinear elliptic problems.
Analysis Of Approximation Methods For Differential And Integral Equations
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Author : Hans-Jürgen Reinhardt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analysis Of Approximation Methods For Differential And Integral Equations written by Hans-Jürgen Reinhardt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is primarily based on the research done by the Numerical Analysis Group at the Goethe-Universitat in Frankfurt/Main, and on material presented in several graduate courses by the author between 1977 and 1981. It is hoped that the text will be useful for graduate students and for scientists interested in studying a fundamental theoretical analysis of numerical methods along with its application to the most diverse classes of differential and integral equations. The text treats numerous methods for approximating solutions of three classes of problems: (elliptic) boundary-value problems, (hyperbolic and parabolic) initial value problems in partial differential equations, and integral equations of the second kind. The aim is to develop a unifying convergence theory, and thereby prove the convergence of, as well as provide error estimates for, the approximations generated by specific numerical methods. The schemes for numerically solving boundary-value problems are additionally divided into the two categories of finite difference methods and of projection methods for approximating their variational formulations.