Calculus of Variations and Geometric Measure Theory

L. Brasco - G. De Philippis - G. Franzina

Positive solutions to the sublinear Lane-Emden equation are isolated

created by brasco on 19 Nov 2019
modified by dephilipp on 05 Jun 2023


Accepted Paper

Inserted: 19 nov 2019
Last Updated: 5 jun 2023

Journal: Comm. Partial Differential Equations
Pages: 31
Year: 2021

ArXiv: 1911.09163 PDF


We prove that on a smooth bounded set, the positive least energy solution of the Lane-Emden equation with sublinear power is isolated. As a corollary, we obtain that the first $q-$eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the $q-$spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.

Keywords: eigenvalues, Lane-Emden equation, constrained critical points, cone condition