Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 51, pp. 1-11.

Title: Convexity of solutions to elliptic PDE's

Authors: Benyam Mebrate (Wollo Univ., Dessie, Ethiopia)
         Giovanni Porru (Univ. of Cagliari, Italy)

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 06, 2024.
Math Subject Classifications: 35E10, 35J60, 35B50.
Key Words: Convexity; maximum principle; boundary blow-up; singular problems.