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A Regularity Result for the p-Laplacian Near Uniform Ellipticity
Carlo Mercuri,
Giuseppe Riey,
Berardino Sciunzi
SIAM Journal on Mathematical Analysis, Volume: 48, Issue: 3, Pages: 2059 - 2075
Swansea University Author: Carlo Mercuri
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DOI (Published version): 10.1137/16m1058546
Abstract
We consider weak solutions to a class of Dirichlet boundary value problems involving the $p$-Laplace operator, and prove that the second weak derivatives have summability as high as it is desirable, provided p is sufficiently close to 2. And as a consequence the Holder exponent of the gradients appr...
Published in: | SIAM Journal on Mathematical Analysis |
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ISSN: | 0036-1410 1095-7154 |
Published: |
Society for Industrial & Applied Mathematics (SIAM)
2016
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Online Access: |
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URI: | https://cronfa.swan.ac.uk/Record/cronfa28298 |
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Abstract: |
We consider weak solutions to a class of Dirichlet boundary value problems involving the $p$-Laplace operator, and prove that the second weak derivatives have summability as high as it is desirable, provided p is sufficiently close to 2. And as a consequence the Holder exponent of the gradients approaches 1. We show that this phenomenon is driven by the classical Calderon-Zygmund constant. We believe that this result is particularly interesting in higher dimensions, and it is related to the optimal regularity of $p$-harmonic mappings. which is still an open question. |
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Keywords: |
quasi-linear elliptic equations, regularity theory, degenerate elliptic equations |
College: |
Faculty of Science and Engineering |
Issue: |
3 |
Start Page: |
2059 |
End Page: |
2075 |