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arXiv · 1602.00122

Existence of very weak solutions to elliptic systems of p-Laplacian type

Miroslav Bulíček·Sebastian Schwarzacher
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Abstract

We study vector valued solutions to non-linear elliptic partial differential equations with $p$-growth. Existence of a solution is shown in case the right hand side is the divergence of a function which is only $q$ integrable, where $q$ is strictly below but close to the duality exponent $p'$. It implies that possibly degenerate operators of $p$-Laplacian type are well posed in a larger class then the natural space of existence. The key novelty here is a refined a priori estimate, that recovers a duality relation between the right hand side and the solution in terms of weighted Lebesgue spaces.

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Miroslav Bulíček, Sebastian Schwarzacher. 2016-01-30. Existence of very weak solutions to elliptic systems of p-Laplacian type. https://doi.org/10.1007/s00526-016-0986-7

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