Remarks on some quasilinear equations with gradient terms and measure data - Archive ouverte HAL
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Pré-Publication, Document De Travail Année : 2013

Remarks on some quasilinear equations with gradient terms and measure data

Résumé

Let ΩRN 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 μ0 and H is an absorption term, i.e. we give two sufficient conditions for existence of a nonnegative solution.
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Dates et versions

hal-00758065 , version 1 (28-11-2012)
hal-00758065 , version 2 (12-02-2013)

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Marie-Françoise Bidaut-Véron, Marta Garcia-Huidobro, Laurent Veron. Remarks on some quasilinear equations with gradient terms and measure data. 2013. ⟨hal-00758065v2⟩
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