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Nonlinear Potential Theory Of Degenerate Elliptic Equations
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Book Synopsis Nonlinear Potential Theory of Degenerate Elliptic Equations by : Juha Heinonen
Download or read book Nonlinear Potential Theory of Degenerate Elliptic Equations written by Juha Heinonen and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained treatment appropriate for advanced undergraduate and graduate students, this volume offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Starting with the theory of weighted Sobolev spaces, the text advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and chapters 8 through 14 form the core of the nonlinear potential theory of superharmonic functions. Topics include balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; harmonic morphisms; and quasiregular mappings. The book concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes.
Book Synopsis Potential Theory for Supersolutions of Degenerate Elliptic Equations by : Tero Kilpeläinen
Download or read book Potential Theory for Supersolutions of Degenerate Elliptic Equations written by Tero Kilpeläinen and published by . This book was released on 1988 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Potential Theory of Degenerate Elliptic Equations by : Juha Heinonen
Download or read book Nonlinear Potential Theory of Degenerate Elliptic Equations written by Juha Heinonen and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. 1993 edition.
Book Synopsis Nonlinear Potential Theory and Weighted Sobolev Spaces by : Bengt O. Turesson
Download or read book Nonlinear Potential Theory and Weighted Sobolev Spaces written by Bengt O. Turesson and published by Springer. This book was released on 2007-05-06 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.
Book Synopsis Degenerate elliptic equations with measure data and nonlinear potentials by : Tero Kilpeläinen
Download or read book Degenerate elliptic equations with measure data and nonlinear potentials written by Tero Kilpeläinen and published by . This book was released on 1990 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Potential Theory - ICPT 94 by : Josef Kral
Download or read book Potential Theory - ICPT 94 written by Josef Kral and published by Walter de Gruyter. This book was released on 2011-10-13 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Book Synopsis Nonlinear Evolution Equations and Potential Theory by : J. Kral
Download or read book Nonlinear Evolution Equations and Potential Theory written by J. Kral and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface.- Gottfried Anger: Direct and inverse problems in potential theory.- Viorel Barbu: Regularity results for sane differential equations associated with maximal monotone operators in Hilbert spaces.- Haim Brezis: Classes d'interpolation associées à un opérateur monotone et applications.- Siegfried Dnümmel: On inverse problems for k-dimensional potentials.- Jozef Ka?ur: Application of Rothe's method to nonlinear parabolic boundary value problems.- Josef Král: Potentials and removability of singularities.- Vladimir Lovicar: Theorem of Fréchet and asymptotically almost periodid solutions of.
Book Synopsis Local And Global Aspects Of Quasilinear Degenerate Elliptic Equations: Quasilinear Elliptic Singular Problems by : Laurent Veron
Download or read book Local And Global Aspects Of Quasilinear Degenerate Elliptic Equations: Quasilinear Elliptic Singular Problems written by Laurent Veron and published by World Scientific. This book was released on 2017-05-05 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of elliptic second-order degenerate quasilinear equations, the model of which is the p-Laplacian, with or without dominant lower order reaction term. Emphasis is put on three aspects:
Book Synopsis Moduli in Modern Mapping Theory by : Olli Martio
Download or read book Moduli in Modern Mapping Theory written by Olli Martio and published by Springer Science & Business Media. This book was released on 2008-11-09 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on recent research papers, this book presents a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. It contains an extensive bibliography.
Book Synopsis Sobolev Spaces in Mathematics I by : Vladimir Maz'ya
Download or read book Sobolev Spaces in Mathematics I written by Vladimir Maz'ya and published by Springer Science & Business Media. This book was released on 2008-12-02 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume mark’s the centenary of the birth of the outstanding mathematician of the 20th century, Sergey Sobolev. It includes new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics.
Book Synopsis Potential Theory Methods for Some Nonlinear Elliptic Equations by : Adisak Seesanea
Download or read book Potential Theory Methods for Some Nonlinear Elliptic Equations written by Adisak Seesanea and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fine Regularity of Solutions of Elliptic Partial Differential Equations by : Jan Malý
Download or read book Fine Regularity of Solutions of Elliptic Partial Differential Equations written by Jan Malý and published by American Mathematical Soc.. This book was released on 1997 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary objective of this monograph is to give a comprehensive exposition of results surrounding the work of the authors concerning boundary regularity of weak solutions of second order elliptic quasilinear equations in divergence form. The book also contains a complete development of regularity of solutions of variational inequalities, including the double obstacle problem, where the obstacles are allowed to be discontinuous. The book concludes with a chapter devoted to the existence theory thus providing the reader with a complete treatment of the subject ranging from regularity of weak solutions to the existence of weak solutions.
Book Synopsis Potential Theory for Fully Nonlinear Elliptic Equations by : Denis A. Labutin
Download or read book Potential Theory for Fully Nonlinear Elliptic Equations written by Denis A. Labutin and published by . This book was released on 1999 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Weighted Sobolev Spaces and Degenerate Elliptic Equations by : Albo Carlos Cavalheiro
Download or read book Weighted Sobolev Spaces and Degenerate Elliptic Equations written by Albo Carlos Cavalheiro and published by Cambridge Scholars Publishing. This book was released on 2023-09-29 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: In various applications, we can meet boundary value problems for elliptic equations whose ellipticity is disturbed in the sense that some degeneration or singularity appears. This bad behavior can be caused by the coefficients of the corresponding differential operator as well as by the solution itself. There are several very concrete problems in various practices which lead to such differential equations, such as glaciology, non-Newtonian fluid mechanics, flows through porous media, differential geometry, celestial mechanics, climatology, and reaction-diffusion problems, among others. This book is based on research by the author on degenerate elliptic equations. This book will be a useful reference source for graduate students and researchers interested in differential equations.
Book Synopsis Nonlinear Potential Theory of Elliptic Equations with Nonstandard Growth by : Teemu Lukkari
Download or read book Nonlinear Potential Theory of Elliptic Equations with Nonstandard Growth written by Teemu Lukkari and published by . This book was released on 2008 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tiivistelmä: Epälineaarinen potentiaaliteoria elliptisille yhtälöille, joissa esiintyy epästandardeja rakenne-ehtoja.
Book Synopsis Nonlinear Potential Theory on Metric Spaces by : Anders Björn
Download or read book Nonlinear Potential Theory on Metric Spaces written by Anders Björn and published by European Mathematical Society. This book was released on 2011 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The $p$-Laplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory, and image processing. Its solutions, called p-harmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs, and Heisenberg groups. Nonlinear potential theory of p-harmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories. This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for interested readers and as a reference text for active researchers. The presentation is rather self contained, but it is assumed that readers know measure theory and functional analysis. The first half of the book deals with Sobolev type spaces, so-called Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study p-harmonic functions on metric spaces, and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space. Each chapter contains historical notes with relevant references, and an extensive index is provided at the end of the book.
Book Synopsis Boundary Value Problems for Nonlinear Elliptic Equations in Divergence Form by : Abubakar Mwasa
Download or read book Boundary Value Problems for Nonlinear Elliptic Equations in Divergence Form written by Abubakar Mwasa and published by Linköping University Electronic Press. This book was released on 2021-02-23 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thesis consists of three papers focussing on the study of nonlinear elliptic partial differential equations in a nonempty open subset Ω of the n-dimensional Euclidean space Rn. We study the existence and uniqueness of the solutions, as well as their behaviour near the boundary of Ω. The behaviour of the solutions at infinity is also discussed when Ω is unbounded. In Paper A, we consider a mixed boundary value problem for the p-Laplace equation ∆pu := div(|∇u| p−2∇u) = 0 in an open infinite circular half-cylinder with prescribed Dirichlet boundary data on a part of the boundary and zero Neumann boundary data on the rest. By a suitable transformation of the independent variables, this mixed problem is transformed into a Dirichlet problem for a degenerate (weighted) elliptic equation on a bounded set. By analysing the transformed problem in weighted Sobolev spaces, it is possible to obtain the existence of continuous weak solutions to the mixed problem, both for Sobolev and for continuous data on the Dirichlet part of the boundary. A characterisation of the boundary regularity of the point at infinity is obtained in terms of a new variational capacity adapted to the cylinder. In Paper B, we study Perron solutions to the Dirichlet problem for the degenerate quasilinear elliptic equation div A(x, ∇u) = 0 in a bounded open subset of Rn. The vector-valued function A satisfies the standard ellipticity assumptions with a parameter 1 < p < ∞ and a p-admissible weight w. For general boundary data, the Perron method produces a lower and an upper solution, and if they coincide then the boundary data are called resolutive. We show that arbitrary perturbations on sets of weighted p-capacity zero of continuous (and quasicontinuous Sobolev) boundary data f are resolutive, and that the Perron solutions for f and such perturbations coincide. As a consequence, it is also proved that the Perron solution with continuous boundary data is the unique bounded continuous weak solution that takes the required boundary data outside a set of weighted p-capacity zero. Some results in Paper C are a generalisation of those in Paper A, extended to quasilinear elliptic equations of the form div A(x, ∇u) = 0. Here, results from Paper B are used to prove the existence and uniqueness of continuous weak solutions to the mixed boundary value problem for continuous Dirichlet data. Regularity of the boundary point at infinity for the equation div A(x, ∇u) = 0 is characterised by a Wiener type criterion. We show that sets of Sobolev p-capacity zero are removable for the solutions and also discuss the behaviour of the solutions at ∞. In particular, a certain trichotomy is proved, similar to the Phragmén–Lindelöf principle.
