A weak solution to quasilinear elliptic problems with perturbed gradient

被引：27

作者：

Azroul, Elhoussine ^{[1
]}

Balaadich, Farah ^{[1
]}

机构：

[1] Fac Sci Dhar El Mehraz, Dept Math, BP 1796, Atlas, Fez, Morocco

来源：

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2021年 / 70卷 / 01期

关键词：

Quasilinear elliptic systems; Weak solutions; Sobolev space; Young measure; DIVERGENCE FORM; EQUATIONS; SYSTEMS; REGULARITY;

D O I：

10.1007/s12215-020-00488-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider weak solutions to the Dirichlet problem where {-div A(x, Du - Theta(u)) = f in Omega, u = 0 on partial derivative Omega, where Theta : R-m -> M-mxn is a continuous function assumed to satisfy a Lipschitz condition. Based on the theory of Young measures, we prove the existence result when f is an element of W--1,W-p' (Omega;R-m).

引用

页码：151 / 166

页数：16

共 28 条

[1]

[Anonymous], 2014, ELECT J DIFFER EQU

[2]

[Anonymous], 1990, WEAK CONVERGENCE MET

[3]

Azroul E., 2018, Moroccan J Pure Appl Anal, V4, P77, DOI [10.1515/mjpaa-2018-0008, DOI 10.1515/MJPAA-2018-0008]

[4] Quasilinear elliptic systems in perturbed form [J].

Azroul, Elhoussine ;

Balaadich, Farah .

INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2019, 10 (02) :255-266

[5]

BALL JM, 1989, LECT NOTES PHYS, V344, P207

[6] MULTIPLE SOLUTIONS FOR ELLIPTIC EQUATIONS INVOLVING A GENERAL OPERATOR IN DIVERGENCE FORM [J].

Bisci, Giovanni Molica ;

Repovs, Dusan .

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2014, 39 (01) :259-273

[7] The p-Laplace system with right-hand side in divergence form: Inner and up to the boundary pointwise estimates [J].

Breit, D. ;

Cianchi, A. ;

Diening, L. ;

Kuusi, T. ;

Schwarzacher, S. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2017, 153 :200-212

[8] Existence of very weak solutions to elliptic systems of p-Laplacian type [J].

Bulicek, Miroslav ;

Schwarzacher, Sebastian .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2016, 55 (03)

[9]

Buliek M., 2015, EXISTENCE UNIQUENESS

[10] Optimal second-order regularity for the p-Laplace system [J].

Cianchi, Andrea ;

Maz'ya, Vladimir G. .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2019, 132 :41-78

← 1 2 3 →