A DIRECT PROOF OF EXISTENCE OF WEAK SOLUTIONS TO ELLIPTIC PROBLEMS

被引：1
|
作者：
Chlebicka, Iwona [1 ]
Karppinen, Arttu [1 ]
Li, Ying [2 ]
机构：
[1] Univ Warsaw, Fac Math Informat & Mech, Ul Banacha 2, PL-02097 Warsaw, Poland
[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2023年 / 62卷 / 02期
关键词：
Existence; elliptic boundary value problems; second order partial differential equations; Musielak-Orlicz spaces; BOUNDARY-VALUE-PROBLEMS; RENORMALIZED SOLUTIONS; ORLICZ; EQUATIONS;
D O I：
10.12775/TMNA.2023.019
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We provide a direct proof of existence and uniqueness of weak solutions to a broad family of strongly nonlinear elliptic equations with lower-order terms. The leading part of the operator satisfies general growth conditions settling the problem in the framework of fully anisotropic and inhomogeneous Musielak-Orlicz spaces generated by an N-function M: Omega x R-d -> left perpendicular 0, infinity). Neither del(2) nor Delta(2) conditions are imposed on M. Our results cover among others problems with anisotropic polynomial, Orlicz, variable exponent, and double phase growth.
引用
收藏
页码：643 / 665
页数：23
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