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Concavity of solutions to degenerate elliptic equations on the sphere

Langford, Mat and Scheuer, Julian 2020. Concavity of solutions to degenerate elliptic equations on the sphere. Communications in Partial Differential Equations 10.1080/03605302.2020.1857404
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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: Published Online
Status: In Press
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: 18 Jan 2021 18:41

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