Symmetry and uniqueness of nonnegative solutions of some problems in the halfspace

Abstract

We derive some 1-D symmetry and uniqueness or non-existence results for nonnegative solutions of some elliptic system in the halfspace ${\mathbb{R}}_{+}^N$ in low dimension. Our method is based upon a combination of Fourier series and Liouville theorems.

Cited by in corpus (2)

• On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results
• Monotonicity of solutions for some nonlocal elliptic problems in half-spaces