VERY WEAK SOLUTIONS OF HIGHER-ORDER DEGENERATE PARABOLIC SYSTEMS

被引：1

作者：

Boegelein, Verena ^{[1
]}

机构：

[1] Univ Erlangen Nurnberg, Dept Math, D-91054 Erlangen, Germany

来源：

ADVANCES IN DIFFERENTIAL EQUATIONS | 2009年 / 14卷 / 1-2期

关键词：

P-LAPLACIAN TYPE; HIGHER INTEGRABILITY; ELLIPTIC-SYSTEMS; REGULARITY; INEQUALITIES; EQUATIONS; MAPPINGS; MINIMA;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider non-linear higher-order parabolic systems whose simplest model is the parabolic p-Laplacean system integral(Omega T) u . phi(t) - <vertical bar D(m)u vertical bar(p-2) D(m)u, D(m)phi > dz = 0 It turns out that the usual regularity assumptions on solutions can be weakened in the sense that going slightly below the natural integrability exponent still yields a classical weak solution. Namely, we prove the existence of some beta > 0 such that D(m)u is an element of L(p-beta) double right arrow D(m)u is an element of L(p+beta).

引用

页码：121 / 200

页数：80

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