Towards a Proof of Bahri-Coron's Type Theorem for Mixed Boundary Value Problems

被引：0

作者：

Alghanemi, Azeb ^{[1
]}

Chaabane, Slim ^{[2
]}

Chtioui, Hichem ^{[2
]}

Soumare, Abdellahi ^{[2
]}

机构：

[1] King Abdulaziz Univ, Fac Sci, Dept Math, POB 80203, Jeddah 21589, Saudi Arabia

[2] Sfax Univ, Fac Sci Sfax, Dept Math, Sfax 3018, Tunisia

来源：

MATHEMATICS | 2023年 / 11卷 / 08期

关键词：

nonlinear elliptic problems; critical nonlinearities; variational structures; mixed boundary conditions; topological methods; CRITICAL SOBOLEV EXPONENT; ELLIPTIC-EQUATIONS;

D O I：

10.3390/math11081955

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a nonlinear variational elliptic problem with critical nonlinearity on a bounded domain of R-n,n = 3 and mixed Dirichlet-Neumann boundary conditions. We study the effect of the domain's topology on the existence of solutions as Bahri-Coron did in their famous work on the homogeneous Dirichlet problem. However, due to the influence of the part of the boundary where the Neumann condition is prescribed, the blow-up picture in the present setting is more complicated and makes the mixed boundary problems different with respect to the homogeneous ones. Such complexity imposes modification of the argument of Bahri-Coron and demands new constructions and extra ideas.

引用

页数：26

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