Electron. J. Differential Equations, Vol. 2024 (2024), No. 51, pp. 1-11.

Convexity of solutions to elliptic PDE's

Benyam Mebrate, Giovanni Porru

Abstract:
This article concerns the convexity or concavity of solutions to special second order elliptic partial differential equations in convex domains. We concentrate our investigation to boundary blow up solutions as well as to solutions of particular singular equations. Following a method due to Korevaar and Kennington, we find a new sufficient condition for proving convexity or concavity. This sufficient condition is useful when the semilinear component of the equation is the sum of two or more terms.

Submitted March 25, 2024. Published September 6, 2024.
Math Subject Classifications: 35E10, 35J60, 35B50.
Key Words: Convexity; maximum principle; boundary blow-up; singular problems.
DOI: 10.58997/ejde.2024.51

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Benyam Mebrate
Department of Mathematics
Wollo University
Dessie, Ethiopia
email: benyam134@gmail.com
Giovanni Porru
Department of Mathematics and Informatics
University of Cagliari
Cagliari, Italy
email: gporru856@gmail.com

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