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Research Article | Open Access

Improvements on overdetermined problems associated to the p-Laplacian

Antonio Greco1( ), Francesco Pisanu2
Department of Mathematics and Computer Science, University of Cagliari, Italy
Department of Computer Science, University Paris 13, France
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Abstract

This work presents some improvements on related papers that investigate certain overdetermined problems associated to elliptic quasilinear operators. Our model operator is the p-Laplacian. Under suitable structural conditions, and assuming that a solution exists, we show that the domain of the problem is a ball centered at the origin. Furthermore we discuss a convenient form of comparison principle for this kind of problems.

Keywords

p-Laplacianoverdetermined problemscomparison principleboundary-point lemma

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Mathematics in Engineering
Volume 4 Issue 3,
June 2022
Pages 1-14
DOI: 10.3934/mine.2022017

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Cite this article:
Greco A, Pisanu F. Improvements on overdetermined problems associated to the p-Laplacian. Mathematics in Engineering, 2022, 4(3): 1-14. https://doi.org/10.3934/mine.2022017

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Received: 03 February 2021
Accepted: 27 April 2021
Published: 15 June 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)