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Elliptic and Parabolic Equations with Discontinuous Coefficients

Elliptic and Parabolic Equations with Discontinuous Coefficients

Antonino Maugeri, Lubomira G. Softova, Dian K. Palagachev

ISBN: 978-3-527-60086-1

Sep 2003

320 pages

Select type: Online Book

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.
BVPS FOR LINEAR OPERATORS WITH DISCONTINUOUS COEFFICIENTS
Examples for Nonsolvable BVPs
The Cordes Condition
Operators with Sobolev Coefficients
Miranda-Talenti Estimate
Elliptic Equations in the Plane
Cauchy-Dirichlet Problem for Parabolic Operators
Oblique Derivative Problem (ODP) for Parabolic Operators with Measurable Coefficients
Elliptic ODPs
LINEAR AND QUASILINEAR OPERATORS WITH VMO COEFFICIENTS
Regular ODP - a Special Case/the General Case
Singular ODP
Parabolic ODP
Quasilinear Operators with VMO Coefficients
NONLINEAR OPERATORS WITH DISCONTINUOUS COEFFICIENTS
Nonlinear Cordes Condition
Nonlinear Elliptic Systems
Parabolic Systems
"...presents various results concerning second-order elliptic and parabolic equations with discontinuous coefficients." (SciTech Book News, Vol. 26, No. 2, June 2002)