Concavity of solutions to degenerate elliptic equations on the sphere

Title: Concavity of solutions to degenerate elliptic equations on the sphere
Creator: Langford, Mat; Scheuer, Julian
Relation: Communications in Partial Differential Equations Vol. 46, Issue 6, p. 1005-1016
Publisher Link: http://dx.doi.org/10.1080/03605302.2020.1857404
Publisher: Taylor & Francis
Resource Type: journal article
Date: 2021
Description: 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.
Subject: degenerate elliptic equations; fully nonlinear PDE; concavity of classical solutions; Euclidean domains
Identifier: http://hdl.handle.net/1959.13/1442558
Identifier: uon:41722
Identifier: ISSN:0360-5302
Language: eng
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