Unique continuation principles in cones under nonzero Neumann boundary conditions

Serena Dipierro; Veronica Felli; Enrico Valdinoci

doi:10.1016/j.anihpc.2020.01.005

Unique continuation principles in cones under nonzero Neumann boundary conditions

Serena Dipierro, Veronica Felli, Enrico Valdinoci

Mathematics and Statistics

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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 language	English
Pages (from-to)	785-815
Number of pages	31
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	37
Issue number	4
DOIs	https://doi.org/10.1016/j.anihpc.2020.01.005
Publication status	Published - 1 Jul 2020

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10.1016/j.anihpc.2020.01.005

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Dipierro et al., 2020 Unique continuation principles in cones under nonzero Neumann boundary conditions
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Partial Differential Equations, free boundaries and applications
Dipierro, S.
Australian Research Council
30/11/18 → 30/11/21
Project: Research
Nonlocal Equations at Work
Dipierro, S. & Valdinoci, E.
Australian Research Council
1/11/11 → 31/12/20
Project: Research

Cite this

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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.",

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AU - Felli, Veronica

AU - Valdinoci, Enrico

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N2 - 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.

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KW - Conical geometry

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JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

SN - 0294-1449

IS - 4

ER -

Unique continuation principles in cones under nonzero Neumann boundary conditions

Abstract

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Partial Differential Equations, free boundaries and applications

Nonlocal Equations at Work

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