Concavity of solutions to degenerate elliptic equations on the sphere

Langford, Mat and Scheuer, Julian ORCID: https://orcid.org/0000-0003-2664-1896 2021. Concavity of solutions to degenerate elliptic equations on the sphere. Communications in Partial Differential Equations 46 (6) , pp. 1005-1016. 10.1080/03605302.2020.1857404

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Abstract

We prove the concavity of classical solutions to a wide class of degenerate elliptic differential equations on strictly convex domains of the unit sphere. The proof employs a suitable two-point maximum principle, a technique which originates in works of Korevaar, Kawohl and Kennington for equations on Euclidean domains. We emphasize that no differentiability of the differential operator is needed, but only some monotonicity and concavity properties.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Taylor & Francis: STM, Behavioural Science and Public Health Titles
ISSN:	0360-5302
Date of First Compliant Deposit:	12 October 2020
Date of Acceptance:	13 July 2020
Last Modified:	03 Dec 2024 22:00
URI:	https://orca.cardiff.ac.uk/id/eprint/135527

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