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Research Article | Open Access

Lewy-Stampacchia inequality for noncoercive parabolic obstacle problems

Fernando Farroni, Gioconda Moscariello( ), Gabriella Zecca
Dipartimento di Matematica e Applicazioni R. Caccioppoli, Università degli Studi di Napoli Federico II, Complesso Universitario di Monte S. Angelo, via Cinthia I-80126 Napoli, Italy
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Abstract

We investigate the obstacle problem for a class of nonlinear and noncoercive parabolic variational inequalities whose model is a Leray–Lions type operator having singularities in the coefficients of the lower order terms. We prove the existence of a solution to the obstacle problem satisfying a Lewy-Stampacchia type inequality.

Keywords

noncoercive evolution problemsobstacle problemspenalizationLewy–Stampacchia inequalityMarcinkiewicz spaces

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Mathematics in Engineering
Volume 5 Issue 4,
August 2023
Pages 1-23
DOI: 10.3934/mine.2023071

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Cite this article:
Farroni F, Moscariello G, Zecca G. Lewy-Stampacchia inequality for noncoercive parabolic obstacle problems. Mathematics in Engineering, 2023, 5(4): 1-23. https://doi.org/10.3934/mine.2023071

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Received: 26 August 2022
Revised: 22 December 2022
Accepted: 22 December 2022
Published: 15 August 2023
©2023 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)