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Article Dans Une Revue Journal of Differential Equations Année : 2022

Weighted p−Laplace approximation of linear and quasi-linear elliptic problems with measure data

Résumé

We approximate the solution to some linear and degenerate quasi-linear problem involving a linear elliptic operator (like the semi-discrete in time implicit Euler approximation of Richards and Stefan equations) with measure right-hand side and heterogeneous anisotropic diffusion matrix. This approximation is obtained through the addition of a weighted p−Laplace term. A well chosen diffeomorphism between R and (−1, 1) is used for the estimates of the approximated solution, and is involved in the above weight. We show that this approximation converges to a weak sense of the problem for general right-hand-side, and to the entropy solution in the case where the right-hand-side is in L 1 .
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Dates et versions

hal-03668635 , version 1 (15-05-2022)

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Robert Eymard, David Maltese, Alain Prignet. Weighted p−Laplace approximation of linear and quasi-linear elliptic problems with measure data. Journal of Differential Equations, 2022, 330, pp.208-236. ⟨10.1016/j.jde.2022.05.012⟩. ⟨hal-03668635⟩
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