Singular elliptic problems with Dirichlet or mixed Dirichlet-Neumann non-homogeneous boundary conditions

• Autorzy: Godoy Tomas

Identyfikatory

DOI

10.7494/OpMath.2023.43.1.19

• Języki publikacji: EN

Abstrakty

EN

Let Ω be a C2 bounded domain in Rn such that ∂Ω = Γ1 ∪ Γ2, where Γ1 and Γ2 are disjoint closed subsets of ∂Ω, and consider the problem −Δu = g(·, u) in Ω, u = τ on Γ1, ∂u ∂ν = η on Γ2, where 0 ≤ τ ∈ W 1 2 ,2(Γ1), η ∈ (H1 0, Γ1(Ω))′, and g : Ω×(0,∞) → R is a nonnegative Carathéodory function. Under suitable assumptions on g and η we prove the existence and uniqueness of a positive weak solution of this problem. Our assumptions allow g to be singular at s = 0 and also at x ∈ S for some suitable subsets S ⊂ Ω. The Dirichlet problem −Δu = g(·, u) in Ω, u = σ on ∂Ω is also studied in the case when 0 ≤ σ ∈ W 1 2 ,2(Ω).

Słowa kluczowe

EN

singular elliptic problems; mixed boundary conditions; weak solutions

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2023
• Tom: Vol. 43, no. 1
• Strony: 19--46
• Opis fizyczny: Bibliogr. 48 poz.

Twórcy

autor

Godoy Tomas

• Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, Av. Medina Allende s/n, Ciudad Universitaria, 5000 Córdoba, Argentina

• https://orcid.org/0000-0002-8804-9137

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)