Calculus of Variations and Geometric Measure Theory
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E. Moreira Dos Santos - G. Nornberg - N. Soave

On unique continuation principles for some elliptic systems

created by soave on 27 Sep 2019

[BibTeX]

Submitted Paper

Inserted: 27 sep 2019
Last Updated: 27 sep 2019

Year: 2019

ArXiv: 1909.07948 PDF

Abstract:

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.

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