Elliptic and Parabolic Equations with Discontinuous Coefficients, Volume 109

Description

This book unifies the different approaches in studying elliptic and parabolic partial differential equations with discontinuous coefficients. To the enlarging market of researchers in applied sciences, mathematics and physics, it gives concrete answers to questions suggested by non-linear models. Providing an up-to date survey on the results concerning elliptic and parabolic operators on a high level, the authors serve the reader in doing further research. Being themselves active researchers in the field, the authors describe both on the level of good examples and precise analysis, the crucial role played by such requirements on the coefficients as the Cordes condition, Campanato's nearness condition, and vanishing mean oscillation condition. They present the newest results on the basic boundary value problems for operators with VMO coefficients and non-linear operators with discontinuous coefficients and state a lot of open problems in the field.Content: Chapter 1.1 Boundary Value Problems for Linear Operators with Discontinuous Coefficients: Examples of Nonsolvable BVPs for Linear Operators with Discontinuous Coefficients (pages 15–19): Chapter 1.2 Boundary Value Problems for Linear Operators with Discontinuous Coefficients: The Cordes Condition (pages 19–34): Chapter 1.3 Boundary Value Problems for Linear Operators with Discontinuous Coefficients: Operators with Sobolev Coefficients (pages 34–39): Chapter 1.4 Boundary Value Problems for Linear Operators with Discontinuous Coefficients: Miranda–Talenti Estimate (pages 39–46): Chapter 1.5 Boundary Value Problems for Linear Operators with Discontinuous Coefficients: Elliptic Equations in the Plane (pages 46–57): Chapter 1.6 Boundary Value Problems for Linear Operators with Discontinuous Coefficients: Cauchy–Dirichlet Problem for Parabolic Operators (pages 57–83): Chapter 1.7 Boundary Value Problems for Linear Operators with Discontinuous Coefficients: Oblique Derivative Problem for Parabolic Operators with Measurable Coefficients (pages 83–92): Chapter 1.8 Boundary Value Problems for Linear Operators with Discontinuous Coefficients: Elliptic Oblique Derivative Problems (pages 92–101): Chapter 2.1 Linear and Quasilinear Operators with VMO Coefficients: Preliminaries and Auxiliary Results (pages 103–116): Chapter 2.2 Linear and Quasilinear Operators with VMO Coefficients: Regular Oblique Derivative Problem — A Special Case (pages 116–135): Chapter 2.3 Linear and Quasilinear Operators with VMO Coefficients: Regular Oblique Derivative Problem — The General Case (pages 135–142): Chapter 2.4 Linear and Quasilinear Operators with VMO Coefficients: Singular Oblique Derivative Problem (pages 142–153): Chapter 2.5 Linear and Quasilinear Operators with VMO Coefficients: Parabolic Oblique Derivative Problem (pages 153–165): Chapter 2.6 Linear and Quasilinear Operators with VMO Coefficients: Quasilinear Operators with VMO Coefficients (pages 165–176): Chapter 3.1 Nonlinear Operators with Discontinuous Coefficients: Nonlinear Cordes Condition (pages 177–188): Chapter 3.2 Nonlinear Operators with Discontinuous Coefficients: Nonlinear Elliptic Systems (pages 188–216): Chapter 3.3 Nonlinear Operators with Discontinuous Coefficients: Parabolic Systems (pages 217–234):