Towards a Proof of Bahri–Coron’s Type Theorem for Mixed Boundary Value Problems

Autor:	Azeb Alghanemi, Slim Chaabane, Hichem Chtioui, Abdellahi Soumaré
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	nonlinear elliptic problems critical nonlinearities variational structures mixed boundary conditions topological methods Mathematics QA1-939
Zdroj:	Mathematics, Vol 11, Iss 8, p 1955 (2023)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math11081955
Popis:	We consider a nonlinear variational elliptic problem with critical nonlinearity on a bounded domain of Rn,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.
Databáze:	Directory of Open Access Journals
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