Generalized Gagliardo-Nirenberg estimates and differentiability of the solutions to monotone nonlinear parabolic systems

被引：7

作者：

Marino, Mario ^{[1
]}

Maugeri, Antonino ^{[1
]}

机构：

[1] Univ Catania, Dept Math & Comp Sci, I-95125 Catania, Italy

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2008年 / 40卷 / 1-3期

关键词：

generalized Sobolev spaces; Gagliardo-Nirenberg estimates; nonlinear parabolic systems; interior differentiability;

D O I：

10.1007/s10898-007-9184-7

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, we are concerned with interior differentiability of weak solutions u to nonlinear parabolic systems with natural growth and coefficients uniformly monotone in Du. Making use of estimates of Gagliardo-Nirenberg's type in generalized Sobolev spaces, we show that u belongs to L-2 (-a, 0, H-2 (B(sigma), R-N)) boolean AND H-1 (-a,0,L-2 (B(sigma), R-N)) (see Theorem 3).

引用

页码：185 / 196

页数：12

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