Symmetry of large solutions for semilinear elliptic equations in a ball

Abstract

In this work we consider the boundary blow-up problem $$\{\begin{array}{ll}\Delta u=f(u)& inB\\ u=+\infty & on\partial B\end{array}$$ where $B$ stands for the unit ball of ${\mathbb{R}}^N$ and $f$ is a locally Lipschitz function which is positive for large values and verifies the Keller-Osserman condition. Under an additional hypothesis on the asymptotic behavior of $f$ we show that all solutions of the above problem are radially symmetric and radially increasing. Our condition is sharp enough to generalize several results in previous literature.

References in corpus (1)

• Symmetry of large solutions of nonlinear elliptic equations in a ball