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On coercivity and irregularity for some nonlinear degenerate elliptic systems

  • Kewei ZhangEmail author
Research Article
  • 34 Downloads

Abstract

We study the ‘universal’ strong coercivity problem for variational integrals of degenerate p-Laplacian type by mixing finitely many homogenous systems. We establish the equivalence between universal p-coercivity and a generalized notion of p-quasiconvex extreme points. We then give sufficient conditions and counterexamples for universal coercivity. In the case of noncoercive systems we give examples showing that the corresponding variational integral may have infinitely many non-trivial minimizers in W 0 1,p which are nowhere C 1 on their supports. We also give examples of universally p-coercive variational integrals in W 0 1,p for p ⩾ with L coefficients for which uniqueminimizers under affine boundary conditions are nowhere C 1.

Keywords

Degenerate p-Laplace system measurable coefficient universal p-strong coercivity subspace without rank-one matrice nowhere C1 minimizers 

MSC

35J45 35J50 35J55 49J10 49N60 

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Copyright information

© Higher Education Press and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Department of MathematicsSwansea UniversitySwanseaUK

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