Boundary Value Problems For Nonlinear Elliptic Equations In Divergence Form

DOWNLOAD

Download Boundary Value Problems For Nonlinear Elliptic Equations In Divergence Form PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Boundary Value Problems For Nonlinear Elliptic Equations In Divergence Form book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Boundary Value Problems For Nonlinear Elliptic Equations In Divergence Form

DOWNLOAD
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 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.

Methods For Analysis Of Nonlinear Elliptic Boundary Value Problems

DOWNLOAD
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.

Convex Analysis And Nonlinear Geometric Elliptic Equations

DOWNLOAD
Author : Ilya J. Bakelman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Convex Analysis And Nonlinear Geometric Elliptic Equations written by Ilya J. Bakelman 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.

Investigations in modem nonlinear analysis rely on ideas, methods and prob lems from various fields of mathematics, mechanics, physics and other applied sciences. In the second half of the twentieth century many prominent, ex emplary problems in nonlinear analysis were subject to intensive study and examination. The united ideas and methods of differential geometry, topology, differential equations and functional analysis as well as other areas of research in mathematics were successfully applied towards the complete solution of com plex problems in nonlinear analysis. It is not possible to encompass in the scope of one book all concepts, ideas, methods and results related to nonlinear analysis. Therefore, we shall restrict ourselves in this monograph to nonlinear elliptic boundary value problems as well as global geometric problems. In order that we may examine these prob lems, we are provided with a fundamental vehicle: The theory of convex bodies and hypersurfaces. In this book we systematically present a series of centrally significant results obtained in the second half of the twentieth century up to the present time. Particular attention is given to profound interconnections between various divisions in nonlinear analysis. The theory of convex functions and bodies plays a crucial role because the ellipticity of differential equations is closely connected with the local and global convexity properties of their solutions. Therefore it is necessary to have a sufficiently large amount of material devoted to the theory of convex bodies and functions and their connections with partial differential equations.

Quasilinear Degenerate And Nonuniformly Elliptic And Parabolic Equations Of Second Order

DOWNLOAD
Author : A. V. Ivanov
language : en
Publisher: American Mathematical Soc.
Release Date : 1984

Quasilinear Degenerate And Nonuniformly Elliptic And Parabolic Equations Of Second Order written by A. V. Ivanov 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 1984 with Mathematics categories.

Oblique Derivative Problems For Elliptic Equations In Conical Domains

DOWNLOAD
Author : Mikhail Borsuk
language : en
Publisher: Springer Nature
Release Date : 2023-05-31

Oblique Derivative Problems For Elliptic Equations In Conical Domains written by Mikhail Borsuk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-31 with Mathematics categories.

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.

Numerical Methods For Nonlinear Elliptic Differential Equations

DOWNLOAD
Author : Klaus Boehmer
language : en
Publisher: OUP Oxford
Release Date : 2010-10-07

Numerical Methods For Nonlinear Elliptic Differential Equations written by Klaus Boehmer and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-07 with Science categories.

Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, creating an exciting interplay between the subjects. This is the first and only book to prove in a systematic and unifying way, stability, convergence and computing results for the different numerical methods for nonlinear elliptic problems. The proofs use linearization, compact perturbation of the coercive principal parts, or monotone operator techniques, and approximation theory. Examples are given for linear to fully nonlinear problems (highest derivatives occur nonlinearly) and for the most important space discretization methods: conforming and nonconforming finite element, discontinuous Galerkin, finite difference, wavelet (and, in a volume to follow, spectral and meshfree) methods. A number of specific long open problems are solved here: numerical methods for fully nonlinear elliptic problems, wavelet and meshfree methods for nonlinear problems, and more general nonlinear boundary conditions. We apply it to all these problems and methods, in particular to eigenvalues, monotone operators, quadrature approximations, and Newton methods. Adaptivity is discussed for finite element and wavelet methods. The book has been written for graduate students and scientists who want to study and to numerically analyze nonlinear elliptic differential equations in Mathematics, Science and Engineering. It can be used as material for graduate courses or advanced seminars.

Regularity Estimates For Nonlinear Elliptic And Parabolic Problems

DOWNLOAD
Author : John Lewis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-03-02

Regularity Estimates For Nonlinear Elliptic And Parabolic Problems written by John Lewis 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 2012-03-02 with Mathematics categories.

The issue of regularity has played a central role in the theory of Partial Differential Equations almost since its inception, and despite the tremendous advances made it still remains a very fruitful research field. In particular considerable strides have been made in regularity estimates for degenerate and singular elliptic and parabolic equations over the last several years, and in many unexpected and challenging directions. Because of all these recent results, it seemed high time to create an overview that would highlight emerging trends and issues in this fascinating research topic in a proper and effective way. The course aimed to show the deep connections between these topics and to open new research directions through the contributions of leading experts in all of these fields.

Solvability Of Nonlinear Equations And Boundary Value Problems

DOWNLOAD
Author : Svatopluk Fucik
language : en
Publisher: Springer Science & Business Media
Release Date : 1981-02-28

Solvability Of Nonlinear Equations And Boundary Value Problems written by Svatopluk Fucik 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 1981-02-28 with Mathematics categories.

Afosr Research The Current Research Program And A Summary Of Research Accomplishments

DOWNLOAD
Author : United States. Air Force. Office of Scientific Research
language : en
Publisher:
Release Date : 1967

Afosr Research The Current Research Program And A Summary Of Research Accomplishments written by United States. Air Force. Office of Scientific Research and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Military research categories.

This report is designed to present the research programs of the Air Force Office of Scientific Research for the information of users of Air Force research, for scientific investigators working in the same or in allied fields, and for the military, scientific and academic, and Government communities at large.

Nonlinear Elliptic Boundary Value Problems

DOWNLOAD
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.