Uniqueness of least energy solutions to a semilinear elliptic equation in ℝ2
Journal
Manuscripta Mathematica
Journal Volume
84
Journal Issue
1
Pages
13-19
Date Issued
1994
Author(s)
Abstract
In this paper, we prove that solutions minimizing the nonlinear functional {Mathematical expression} among the Sobolev space H 0 1 (Ω) are unique when Ω is bounded convex domain in ℝ2. This uniqueness's results is equivalent to saying that solutions obtained from the Mountain Pass Lemma for the equation Δu+u p =0 are unique. We also prove that the level set of the unique solution is strictly convex. © 1994 Springer-Verlag.
SDGs
Type
journal article