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Article Dans Une Revue Applicable Analysis Année : 2022

Existence and regularity results for some fully nonlinear singular or degenerate equation

Résumé

In this article we prove existence, uniqueness and regularity for the singular equation |∇u| α (F (D 2 u) + h(x) • ∇u) + c(x)|u| α u + p(x)u −γ = 0 in Ω u > 0 in Ω, u = 0 on ∂Ω when p is some continuous and positive function, c and h are continuous, α > −1 and F is Fully non linear elliptic. Some conditions on the first eigenvalue for the operator −|∇u| α (F (D 2 u) + h(x) • ∇u) − c(x)|u| α u are required. The results generalize the well known results of Lazer and McKenna.
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Dates et versions

hal-03808930 , version 1 (10-10-2022)

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Cheikhou Oumar Ndaw. Existence and regularity results for some fully nonlinear singular or degenerate equation. Applicable Analysis, In press, ⟨10.1080/00036811.2022.2030721⟩. ⟨hal-03808930⟩
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