Calculus of Variations and Geometric Measure Theory

E. Moreira Dos Santos - G. Nornberg - N. Soave

On unique continuation principles for some elliptic systems

created by soave on 27 Sep 2019
modified on 16 Mar 2021


Published Paper

Inserted: 27 sep 2019
Last Updated: 16 mar 2021

Journal: Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire
Year: 2019
Doi: 10.1016/j-anihpc.2020.12.001

ArXiv: 1909.07948 PDF


In this paper we prove unique continuation principles for some systems of elliptic partial differential equations satisfying a suitable superlinearity condition. As an application, we obtain nonexistence of nontrivial (not necessarily positive) radial solutions for the Lane-Emden system posed in a ball, in the critical and supercritical regimes. Some of our results also apply to general fully nonlinear operators, such as Pucci's extremal operators, being new even for scalar equations.