Sobolev-Dirichlet problem for quasilinear elliptic equations in generalized Orlicz-Sobolev spaces

被引：8

作者：

Benyaiche, Allami ^{[1
]}

Khlifi, Ismail ^{[1
]}

机构：

[1] Ibn Tofail Univ, Dept Math, BP 133, Kenitra, Morocco

来源：

POSITIVITY | 2021年 / 25卷 / 03期

关键词：

Generalized Phi-functions; Generalized Orlicz-Sobolev spaces; Obstacle problem; Sobolev-Dirichlet problem; Harnack inequality; Holder continuity; SETS; OBSTACLE;

D O I：

10.1007/s11117-020-00789-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove existence, uniqueness, and local regularity of the solution to the Sobolev-Dirichlet problem for quasilinear elliptic equations in the generalized Orlicz-Sobolev spaces on domains, not necessarily bounded, of R-N. Our approach is based on solving the obstacle problem and using the Harnack inequality.

引用

页码：819 / 841

页数：23

共 50 条

[1] Sobolev–Dirichlet problem for quasilinear elliptic equations in generalized Orlicz–Sobolev spaces
Allami Benyaiche
Ismail Khlifi
[J]. Positivity, 2021, 25 : 819 - 841
[2] Harnack Inequality for Quasilinear Elliptic Equations in Generalized Orlicz-Sobolev Spaces
Benyaiche, Allami
Khlifi, Ismail
[J]. POTENTIAL ANALYSIS, 2020, 53 (02) : 631 - 643
[3] Harnack Inequality for Quasilinear Elliptic Equations in Generalized Orlicz-Sobolev Spaces
Allami Benyaiche
Ismail Khlifi
[J]. Potential Analysis, 2020, 53 : 631 - 643
[4] Quasilinear elliptic non-homogeneous Dirichlet problems through Orlicz-Sobolev spaces
Bonanno, Gabriele
Bisci, Giovanni Molica
Radulescu, Vicentiu D.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (12) : 4441 - 4456
[5] Nonlinear eigenvalues for a quasilinear elliptic system in Orlicz-Sobolev spaces
Huentutripay, Jorge
Manasevich, Raul
[J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2006, 18 (04) : 901 - 929
[6] On quasilinear elliptic systems with growth conditions in Orlicz-Sobolev spaces
Balaadich, Farah
Azroul, Elhoussine
[J]. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2023, 17 (02): : 994 - 1005
[7] ON SOME QUASILINEAR EQUATIONS OF KIRCHHOFF TYPE: A GENERALIZED ORLICZ-SOBOLEV SPACES SETTING
Aouaoui, Sami
[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2013, 14 (02) : 263 - 280
[8] L∞-bounds for elliptic equations on Orlicz-Sobolev spaces
Fuchs, M
Li, GB
[J]. ARCHIV DER MATHEMATIK, 1999, 72 (04) : 293 - 297
[9] A STRONGLY NONLINEAR ELLIPTIC PROBLEM IN ORLICZ-SOBOLEV SPACES
GOSSEZ, JP
[J]. PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS, 1986, 45 : 455 - 462
[10] Radial solutions of quasilinear equations in Orlicz-Sobolev type spaces
Santos, Jefferson A.
Soares, Sergio H. M.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 428 (02) : 1035 - 1053

← 1 2 3 4 5 →