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arXiv · 1909.07948

On unique continuation principles for some elliptic systems

Ederson Moreira dos Santos·Gabrielle Nornberg·Nicola Soave
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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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Ederson Moreira dos Santos, Gabrielle Nornberg, Nicola Soave. 2019-09-17. On unique continuation principles for some elliptic systems. https://doi.org/10.1016/j.anihpc.2020.12.001

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