Elliptic and Parabolic Equations with Discontinuous Coefficients

Elliptic and Parabolic Equations with Discontinuous Coefficients

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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.show more

Product details

  • Other digital | 320 pages
  • 1 x 1 x 1mm
  • Wiley-VCH Verlag GmbH
  • Weinheim, Germany
  • 3527600868
  • 9783527600861

Table of contents

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 Systemsshow more

Review quote

"...presents various results concerning second-order elliptic and parabolic equations with discontinuous coefficients." (SciTech Book News, Vol. 26, No. 2, June 2002)show more