Regular solutions for nonlinear elliptic equations, with convective terms, in Orlicz spaces

被引：3
作者：
Barletta, G. [1 ]
Tornatore, E. [2 ]
机构：
[1] Univ Mediterranea Reggio Calabria, Dipartimento Ingn Civile Energia Ambiente & Mat, I-89122 Reggio Di Calabria, Italy
[2] Univ Palermo, Dept Math & Comp Sci, Palermo, Italy
来源：
MATHEMATISCHE NACHRICHTEN | 2023年 / 296卷 / 06期
关键词：
gradient dependence; nonlinear elliptic equations; Orlicz-Sobolev spaces; sub-supersolution; POSITIVE SOLUTIONS; EXISTENCE; DEPENDENCE; GROWTH;
D O I：
10.1002/mana.202100398
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We establish some existence and regularity results to the Dirichlet problem, for a class of quasilinear elliptic equations involving a partial differential operator, depending on the gradient of the solution. Our results are formulated in the Orlicz-Sobolev spaces and under general growth conditions on the convection term. The sub- and supersolutions method is a key tool in the proof of the existence results.
引用
收藏
页码：2203 / 2213
页数：11
相关论文
共 24 条
[1]  
Adams R.A., 1975, Sobolev Spaces
[2]  
Baldelli L., 2020, NONLINEAR ANAL-THEOR, V198, P22
[3]   Elliptic problems with convection terms in Orlicz spaces [J].
Barletta, Giuseppina ;
Tornatore, Elisabetta .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 495 (02)
[4]   Dirichlet problems for fully anisotropic elliptic equations [J].
Barletta, Giuseppina ;
Cianchi, Andrea .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2017, 147 (01) :25-60
[5]   Quasilinear elliptic equations with a source reaction term involving the function and its gradient and measure data [J].
Bidaut-Veron, Marie-Francoise ;
Nguyen, Quoc-Hung ;
Veron, Laurent .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2020, 59 (05)
[6]   A pocket guide to nonlinear differential equations in Musielak-Orlicz spaces [J].
Chlebicka, Iwona .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2018, 175 :1-27
[7]  
Cianchi A, 1997, COMMUN PART DIFF EQ, V22, P1629
[8]   Orlicz-Sobolev boundary trace embeddings [J].
Cianchi, Andrea .
MATHEMATISCHE ZEITSCHRIFT, 2010, 266 (02) :431-449
[9]   Positive solutions of quasi-linear elliptic equations with dependence on the gradient [J].
Faraci, F. ;
Motreanu, D. ;
Puglisi, D. .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 54 (01) :525-538
[10]   Existence results for nonlinear elliptic equations with Leray-Lions operator and dependence on the gradient [J].
Faria, L. F. O. ;
Miyagaki, O. H. ;
Motreanu, D. ;
Tanaka, M. .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 96 :154-166
123