Format:
Online Ressource
ISBN:
044453217X
,
9780444532176
,
0080557317
,
9780080557311
,
1281144983
,
9781281144980
,
0444532412
,
9780444532411
Series Statement:
Handbook of Differential Equations: Stationary Partial Differential Equations
Content:
This handbook is the sixth and last volume in the series devoted to stationary partial differential equations. The topics covered by this volume include in particular domain perturbations for boundary value problems, singular solutions of semi-linear elliptic problems, positive solutions to elliptic equations on unbounded domains, symmetry of solutions, stationary compressible Navier-Stokes equation, Lotka-Volterra systems with cross-diffusion, fixed point theory for elliptic boundary value problems. * Collection of self contained, state-of-the-art surveys * Written by well-known experts in the field * Informs and updates on all the latest developments
Note:
Includes indexes
,
Front cover; Title Page; Copyright Page; Preface; List of Contributors; Table of contents; Chapter 1. Domain Perturbation for Linear and Semi-Linear Boundary Value Problems; 1 Introduction; 2 Elliptic boundary value problems in divergence form; 3 Semi-linear elliptic problems; 4 Abstract results on linear operators; 5 Perturbations for linear Dirichlet problems; 6 Varying domains and Robin boundary conditions; 7 Neumann problems on varying domains; 8 Approximation by smooth data and domains; 9 Perturbation of semi-linear problems; References
,
Chapter 2. Singular Solutions of Semi-Linear Elliptic Problems1 Introduction; 2 Perturbation of singular solutions; 3 Reaction on the boundary; 4 A fourth-order variant of the Gelfand problem; References; Chapter 3. Positive Solutions to Semi-Linear and Quasi-Linear Elliptic Equations on Unbounded Domains; 1 Introduction and model results; 2 Background, framework and auxiliary facts; 3 Exterior domains. Divergence-type equations; 4 Cone-like domains; 5 Exterior domains. Nondivergence-type equations; 6 Quasi-linear equations; A Appendix. Extended Dirichlet space
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B Appendix. Improved Hardy's inequalityReferences; Chapter 4. Symmetry of Solutions of Elliptic Equations via Maximum Principles; 1 Introduction; 2 Moving-plane method; 3 Break of radial symmetry; 4 Partial symmetry results; 5 Symmetry of solutions of p-Laplace equations; References; Chapter 5. Stationary Boundary Value Problems for Compressible Navier--Stokes Equations; 1 Introduction; 2 Equations of viscous compressible fluid dynamics; 3 Mathematical aspects of the problem; 4 Mathematical preliminaries; 5 Boundary value problems for transport equations
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6 Transport equations with discontinuous coefficient7 Isentropic flows with adiabatic constants gamma in (4/3,5/3]; 8 Estimate of a Green potential. Proof of Theorem 7.6; 9 Outflow--inflow problem; 10 Proof of Theorem 5.5; A Appendix. Proof of Lemmas 10.1 and 10.2; B Appendix. Proof of Lemma 10.3; References; Chapter 6. Positive Solutions for Lotka--Volterra Systems with Cross-Diffusion; 1 Introduction; 2 Positive steady states of competition model with cross-diffusion; 3 Positive steady states of prey--predator model with cross-diffusion
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4 Multiple existence of positive steady states for prey--predator models with cross-diffusionReferences; Chapter 7. Fixed Point Theory and Elliptic Boundary Value Problems; 1 Fixed point theorems; 2 Elliptic boundary value problems; 3 Single semi-linear equations; 4 Systems of semi-linear equations; 5 The m-Laplacians as principal parts; References; Author Index; Subject Index;
,
1. Domain Perturbation for Linear and Semi-Linear Boundary Value Problems, D. Daners. -- 2. Singular solutions of semi-linear elliptic problems J. D̀vila. -- 3. Positive solutions to semi- linear and quasi-linear elliptic equations on unbounded domains, V. Kondratiev, V. Liskevich and Z. Sobol. -- 4. Symmetry of solutions of elliptic equations via maximum principles, F. Pacella and M. Ramaswamy. -- 5. Stationary Boundary Value Problems for Compressible Navier-Stokes equations, P.I. Plotnikov and J. Sokolowski. -- 6. Positive Solutions for Lotka-Volterra Systems with Cross- Diffusion, Y. Yamada. -- 7. Fixed Point Theory and Elliptic Boundary Value Problems, H. Zou.
Additional Edition:
ISBN 1281144983
Additional Edition:
ISBN 0444532412
Additional Edition:
ISBN 044453217X
Additional Edition:
Erscheint auch als Druck-Ausgabe Handbook of differential equations Oxford : Elsevier, 2008
Additional Edition:
Druckausg. Handbook of differential equations ; Stationary partial differential equations, 6 Amsterdam : Elsevier, 2008 ISBN 9780444532411
Language:
English
Subjects:
Mathematics
Keywords:
Partielle Differentialgleichung
;
Partielle Differentialgleichung
;
Electronic books
;
Electronic books
URL:
Volltext
(lizenzpflichtig)
Author information:
Chipot, Michel 1949-
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