Existence and improved regularity for a nonlinear system with collapsing ellipticity

Edgard A. Pimentel; Jose Miguel Urbano

doi:10.2422/2036-2145.201903_006

Existence and improved regularity for a nonlinear system with collapsing ellipticity

Edgard A. Pimentel, Jose Miguel Urbano

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We study a nonlinear system made up of an elliptic equation of blended singular/degenerate type and Poisson's equation with a lowly integrable source. We prove the existence of a weak solution in any space dimension and, chiefly, derive an improved C1,Log-Lip regularity estimate using tangential analysis methods. The system illustrates a sophisticated version of the proverbial thermistor problem and our results are new even in simpler modelling scenarios.

Original language	English (US)
Pages (from-to)	1385-1400
Number of pages	16
Journal	Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume	22
Issue number	3
DOIs	https://doi.org/10.2422/2036-2145.201903_006
State	Published - Jan 1 2021
Externally published	Yes

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Generated from Scopus record by KAUST IRTS on 2023-02-15

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AU - Urbano, Jose Miguel

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AB - We study a nonlinear system made up of an elliptic equation of blended singular/degenerate type and Poisson's equation with a lowly integrable source. We prove the existence of a weak solution in any space dimension and, chiefly, derive an improved C1,Log-Lip regularity estimate using tangential analysis methods. The system illustrates a sophisticated version of the proverbial thermistor problem and our results are new even in simpler modelling scenarios.

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Existence and improved regularity for a nonlinear system with collapsing ellipticity

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