Radial Symmetry of Large Solutions of Semilinear Elliptic Equations with Convection

TL;DR

This paper investigates conditions for radial symmetry of large solutions in semilinear elliptic equations with convection, providing sharp criteria that are independent of the solutions' growth rate at infinity.

Contribution

It establishes precise conditions ensuring radial symmetry of solutions, extending understanding beyond growth rate dependencies in elliptic equations with convection.

Findings

Identifies sharp conditions for radial symmetry

Results are independent of solution growth rate at infinity

Provides criteria applicable to a broad class of equations

Abstract

We study radial symmetry of large solutions of the semi-linear elliptic problem \Delta u + \nabla h.\nabla u = f(|x|,u), and we provide sharp conditions under which the problem has a radial solution. The result is independent of the rate of growth of the solution at infinity.