Nonlinear Elliptic Boundary Value Problems
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Methods For Analysis Of Nonlinear Elliptic Boundary Value Problems
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Author : I. V. Skrypnik
language : en
Publisher: American Mathematical Soc.
Release Date : 1994-01-01
Methods For Analysis Of Nonlinear Elliptic Boundary Value Problems written by I. V. Skrypnik and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.
The theory of nonlinear elliptic equations is currently one of the most actively developing branches of the theory of partial differential equations. This book investigates boundary value problems for nonlinear elliptic equations of arbitrary order. In addition to monotone operator methods, a broad range of applications of topological methods to nonlinear differential equations is presented: solvability, estimation of the number of solutions, and the branching of solutions of nonlinear equations. Skrypnik establishes, by various procedures, a priori estimates and the regularity of solutions of nonlinear elliptic equations of arbitrary order. Also covered are methods of homogenization of nonlinear elliptic problems in perforated domains. The book is suitable for use in graduate courses in differential equations and nonlinear functional analysis.
Nonlinear Elliptic Boundary Value Problems
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Author : I. V. Skrypnik
language : en
Publisher:
Release Date : 1986
Nonlinear Elliptic Boundary Value Problems written by I. V. Skrypnik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Boundary value problems categories.
Nonlinear Elliptic Boundary Value Problems And Their Applications
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Author : H Begehr
language : en
Publisher: CRC Press
Release Date : 1996-05-15
Nonlinear Elliptic Boundary Value Problems And Their Applications written by H Begehr and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-15 with Mathematics categories.
Nonlinear Elliptic Boundary Value Problems
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Author : Igor V. SKRYPNIK
language : en
Publisher:
Release Date : 1986-01-01
Nonlinear Elliptic Boundary Value Problems written by Igor V. SKRYPNIK and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-01-01 with categories.
Boundary Value Problems For Nonlinear Elliptic Equations In Divergence Form
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Author : Abubakar Mwasa
language : en
Publisher: Linköping University Electronic Press
Release Date : 2021-02-23
Boundary Value Problems For Nonlinear Elliptic Equations In Divergence Form written by Abubakar Mwasa and has been published by Linköping University Electronic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-23 with Electronic books categories.
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.
Numerical Solution Of Nonlinear Elliptic Problems Via Preconditioning Operators
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Author : István Faragó
language : en
Publisher: Nova Publishers
Release Date : 2002
Numerical Solution Of Nonlinear Elliptic Problems Via Preconditioning Operators written by István Faragó and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators - Theory & Applications
Polyharmonic Boundary Value Problems
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Author : Filippo Gazzola
language : en
Publisher: Springer
Release Date : 2010-05-26
Polyharmonic Boundary Value Problems written by Filippo Gazzola and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-26 with Mathematics categories.
This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references.
Boundary Value Problems For Nonlinear Elliptic Equations In High Dimensional Domains
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Author : Guochun Wen
language : en
Publisher:
Release Date : 2004
Boundary Value Problems For Nonlinear Elliptic Equations In High Dimensional Domains written by Guochun Wen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Boundary value problems categories.
Boundary Value Problems For Elliptic Equations And Systems
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Author : Guo Chun Wen
language : en
Publisher: Chapman & Hall/CRC
Release Date : 1990
Boundary Value Problems For Elliptic Equations And Systems written by Guo Chun Wen and has been published by Chapman & Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
This monograph mainly deals with several boundary value problems for linear and nonlinear elliptic equations and systems by using function theoretic methods. The established theory is systematic, the considered equations and systems, boundary conditions and domains are rather general. Various methods are used. As an application, the existence of nonlinear quasiconformal mappings onto canonical domains is proved.
Orientation And The Leray Schauder Theory For Fully Nonlinear Elliptic Boundary Value Problems
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Author : Patrick Fitzpatrick
language : en
Publisher: American Mathematical Soc.
Release Date : 1993-01-01
Orientation And The Leray Schauder Theory For Fully Nonlinear Elliptic Boundary Value Problems written by Patrick Fitzpatrick and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Mathematics categories.
The aim of this work is to develop an additive, integer-valued degree theory for the class of quasilinear Fredholm mappings. This class is sufficiently large that, within its framework, one can study general fully nonlinear elliptic boundary value problems. A degree for the whole class of quasilinear Fredholm mappings must necessarily accommodate sign-switching of the degree along admissible homotopies. The authors introduce ''parity'', a homotopy invariant of paths of linear Fredholm operators having invertible endpoints. The parity provides a complete description of the possible changes in sign of the degree and thereby permits use of the degree to prove multiplicity and bifurcation theorems for quasilinear Fredholm mappings. Applications are given to the study of fully nonlinear elliptic boundary value problems.