NDLI: On coercivity and irregularity for some nonlinear degenerate elliptic systems

Content Provider	Springer Nature Link
Author	Zhang, Kewei
Copyright Year	2008
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 $^{1}$.
Starting Page	599
Ending Page	642
Page Count	44
File Format	PDF
ISSN	16733452
Journal	Frontiers of Mathematics in China
Volume Number	3
Issue Number	4
e-ISSN	16733576
Language	English
Publisher	SP Higher Education Press
Publisher Date	2008-10-23
Publisher Institution	Chinese Universities
Publisher Place	Heidelberg
Access Restriction	Subscribed
Subject Keyword	Degenerate p-Laplace system measurable coefficient universal p-strong coercivity subspace without rank-one matrice nowhere C $^{1}$ minimizers Variational methods for elliptic systems Free problems in two or more independent variables Regularity of solutions Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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