Remarks on some quasilinear equations with gradient terms and measure data
Résumé
Let Ω⊂RN be a smooth bounded domain, H a Caratheodory function defined in Ω×R×RN, and μ a bounded Radon measure in Ω. We study the problem% −Δpu+H(x,u,∇u)=μin Ω,u=0on ∂Ω, where Δp is the p-Laplacian (p>1), and we emphasize the case H(x,u,∇u)=±|∇u|q (q>0). We obtain an existence result under subcritical growth assumptions on H, we give necessary conditions of existence in terms of capacity properties, and we prove removability results of eventual singularities. In the supercritical case, when μ≧0 and H is an absorption term, i.e. we give two sufficient conditions for existence of a nonnegative solution.
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