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Existence of very weak solutions to elliptic systems of p-Laplacian type
Type of publication: Article
Citation:
Publication status: Published
Journal: Calc. Var. Partial Differential Equations
Volume: 55
Number: 3
Year: 2016
Pages: 55:52
DOI: 10.1007/s00526-016-0986-7
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.
Preprint project: MORE
Preprint year: 2016
Preprint number: 06
Preprint ID: MORE/2016/06
Keywords:
Authors Bulíček, Miroslav
Schwarzacher, Sebastian
Added by: [MB]
Total mark: 0
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  • buli-schw-journal.pdf
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