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arXiv · 2406.10762

Analysis and approximation of elliptic problems with Uhlenbeck structure in convex polytopes

Tadele Mengesha·Enrique Otarola·Abner J. Salgado
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Abstract

We prove the well posedness in weighted Sobolev spaces of certain linear and nonlinear elliptic boundary value problems posed on convex domains and under singular forcing. It is assumed that the weights belong to the Muckenhoupt class $A_p$ with $p \in (1,\infty$). We also propose and analyze a convergent finite element discretization for the nonlinear elliptic boundary value problems mentioned above. As an instrumental result, we prove that the discretization of certain linear problems are well posed in weighted spaces.

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Tadele Mengesha, Enrique Otarola, Abner J. Salgado. 2024-06-16. Analysis and approximation of elliptic problems with Uhlenbeck structure in convex polytopes. https://arxiv.org/abs/2406.10762

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