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Article Dans Une Revue Calculus of Variations and Partial Differential Equations Année : 2020

Uniform W 1,p estimates for an elliptic operator with Robin boundary condition in a C 1 domain

Résumé

We consider the Robin boundary value problem div(A∇u) = divf + F in Ω, C 1 domain, with (A∇u − f) · n + αu = g on Γ, where the matrix A belongs to V M O(R 3), and discover the uniform estimates on u W 1,p (Ω) , with 1 < p < ∞, independent on α. At the difference with the case p = 2, which is simpler, we call here the weak reverse Hölder inequality. This estimates show that the solution of Robin problem converges strongly to the solution of Dirichlet (resp. Neumann) problem in corresponding spaces when the parameter α tends to ∞ (resp. 0).
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Dates et versions

hal-02523940 , version 1 (06-11-2023)

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Chérif Amrouche, C Conca, A. Ghosh, T. Ghosh. Uniform W 1,p estimates for an elliptic operator with Robin boundary condition in a C 1 domain. Calculus of Variations and Partial Differential Equations, 2020, ⟨10.1007/s00526-020-1713-y⟩. ⟨hal-02523940⟩
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