Higher differentiability and integrability for some nonlinear elliptic systems with growth coefficients in BMO

被引：1

作者：

Moscariello, Gioconda ^{[1
]}

Pascale, Giulio ^{[1
]}

机构：

[1] Univ Napoli Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, Via Cintia, I-80126 Naples, Italy

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2024年 / 63卷 / 04期

关键词：

35B65; 35R05; 42B25; WEAK SOLUTIONS; PARTIAL REGULARITY; SINGULAR SET; EQUATIONS; MINIMIZERS; GRADIENT; INTEGRALS; CALCULUS; MINIMA; SPACES;

D O I：

10.1007/s00526-024-02685-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider local solutionsuof nonlinear elliptic systems of the type divA(x,Du)=divFin Omega subset of R-n where u:Omega -> R(N)is in a weightedW1,plocspace, with p >= 2,Fis in a weightedW1,2locspace andx -> A(x,xi)has growth coefficients in the space of functions with bounded meanoscillation. We prove higher differentiability of uin the sense that the nonlinear expression ofits gradientV mu(Du):=(mu 2+|Du|2)p-24Du, with 0<mu <= 1, is weakly differentiable with D(V mu(Du))in a weightedL2locspace. Moreover we derive some local Calder & oacute;n-estimates when the source term is not necessarily differentiable. Global estimates for a suitable Dirichlet problem are also available

引用

页数：47

共 70 条

[1] REGULARITY FOR MINIMIZERS OF NON-QUADRATIC FUNCTIONALS - THE CASE 1-LESS-THAN-P-LESS-THAN-2 [J].