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L r Estimates for Degenerate Elliptic Problems

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Abstract

We prove L r estimates for the Dirichlet problem −div(a(x,u,Du))=f with f in L q for 1≤q≤+∞, where the operator satisfies α(|s|)|ξ|p≤〈a(x,s,ξ),ξ〉 with p>1. These estimates are obtained without symmetrization and are sharp in some cases.

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  1. Centre Universitaire de Bourges, rue Gaston Berger, 18000, Bourges, France

    Nathalie Grenon

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  1. Nathalie Grenon
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Grenon, N. L r Estimates for Degenerate Elliptic Problems. Potential Analysis 16, 387–392 (2002). https://doi.org/10.1023/A:1014895230754

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