On coercivity and irregularity for some nonlinear
degenerate elliptic systems

doi:10.1007/s11464-008-0036-7

Frontiers of Mathematics in China

0, Vol.

Issue (): 599-642 https://doi.org/10.1007/s11464-008-0036-7

本期目录

On coercivity and irregularity for some nonlinear degenerate elliptic systems

ZHANG Kewei

Department of Mathematics, Swansea University;

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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 W₀^1,p which are nowhere C¹ on their supports. We also give examples of universally p-coercive variational integrals in W₀^1,p for p ≥ 2 with L^∞ coefficients for which unique minimizers under affine boundary conditions are nowhere C¹.

出版日期: 2008-12-05

引用本文:

. On coercivity and irregularity for some nonlinear degenerate elliptic systems[J]. Frontiers of Mathematics in China, 0, (): 599-642.
ZHANG Kewei. On coercivity and irregularity for some nonlinear degenerate elliptic systems. Front. Math. China, 0, (): 599-642.

链接本文:

https://academic.hep.com.cn/fmc/CN/10.1007/s11464-008-0036-7
https://academic.hep.com.cn/fmc/CN/Y0/V/I/599

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