Unique continuation principles in cones under nonzero Neumann boundary conditions

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Abstract

We consider an elliptic equation in a cone, endowed with (possibly inhomogeneous) Neumann conditions. The operator and the forcing terms can also allow non-Lipschitz singularities at the vertex of the cone. In this setting, we provide unique continuation results, both in terms of interior and boundary points. The proof relies on a suitable Almgren-type frequency formula with remainders. As a byproduct, we obtain classification results for blow-up limits.

Original languageEnglish
Pages (from-to)785-815
Number of pages31
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume37
Issue number4
DOIs
Publication statusPublished - 1 Jul 2020

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