Calculus of Variations and Geometric Measure Theory

H. Chan - M. M. González - Y. Huang - E. Mainini - B. Volzone

Uniqueness of entire ground states for the fractional plasma problem

created by mainini on 04 Mar 2020
modified on 01 Dec 2020


Published Paper

Inserted: 4 mar 2020
Last Updated: 1 dec 2020

Journal: Calc. Var. Partial Differential Equations
Volume: 59
Number: 195
Year: 2020
Doi: 10.1007/s00526-020-01845-y

ArXiv: 2003.01093 PDF


We establish uniqueness of vanishing radially decreasing entire solutions, which we call ground states, to some semilinear fractional elliptic equations. In particular, we treat the fractional plasma equation and the supercritical power nonlinearity. As an application, we deduce uniqueness of radial steady states for nonlocal aggregation-diffusion equations of Keller-Segel type, even in the regime that is dominated by aggregation.