On Solutions of Nonlinear Elliptic Equations with L1-Data in Unbounded Domains

被引：0

作者：

Kozhevnikova, L. M. ^{[1
,2
]}

机构：

[1] Ufa Univ Sci & Technol, Sterlitamak Branch, Sterlitamak 453103, Russia

[2] Kazan Volga Reg Fed Univ, Elabuga Branch, Yelabuga 423600, Tatarstan, Russia

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2023年 / 44卷 / 05期

关键词：

quasilinear elliptic equation; entropy solution; equivalence; renormalized solution; unbounded domain; nonreflexive space; Musielak-Orlicz space; RENORMALIZED SOLUTIONS; ENTROPY; EXISTENCE;

D O I：

10.1134/S1995080223050372

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, we consider second-order elliptic equations with nonlinearities determined by Musielak-Orlicz functions and summable right-hand side. The equivalence of entropy solutions and renormalized solutions of the Dirichlet problem in arbitrary unbounded domains with Lipschitz boundary is established. The existence and uniqueness of both entropy solutions and renormalized solutions are proved in nonreflexiveMusielak-Orlicz-Sobolev spaces.

引用

页码：1879 / 1901

页数：23

共 20 条

[1] Gossez's approximation theorems in Musielak-Orlicz-Sobolev spaces [J].