Measure data elliptic problems with generalized Orlicz growth

被引：7

作者：

Chlebicka, Iwona ^{[1
]}

机构：

[1] Univ Warsaw, Fac Math Informat & Mech, Ul Banacha 2, PL-02097 Warsaw, Poland

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2023年 / 153卷 / 02期

关键词：

Capacity; elliptic PDEs; measure data problems; Musielak-Orlicz spaces; Orlicz-Sobolev spaces; very weak solutions; RIGHT-HAND SIDE; RENORMALIZED SOLUTIONS; PARABOLIC EQUATIONS; VARIABLE EXPONENTS; ENTROPY SOLUTIONS; SOBOLEV SPACES; EXISTENCE; REGULARITY; FUNCTIONALS; UNIQUENESS;

D O I：

10.1017/prm.2022.6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study nonlinear measure data elliptic problems involving the operator of generalized Orlicz growth. Our framework embraces reflexive Orlicz spaces, as well as natural variants of variable exponent and double-phase spaces. Approximable and renormalized solutions are proven to exist and coincide for arbitrary measure datum and to be unique when for a class of data being diffuse with respect to a relevant nonstandard capacity. A capacitary characterization of diffuse measures is provided.

引用

页码：588 / 618

页数：31

共 71 条

[1] Regularity results for stationary electro-rheological fluids [J].