1. Unique continuation principles in cones under nonzero Neumann boundary conditions
- Author
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Veronica Felli, Enrico Valdinoci, Serena Dipierro, Dipierro, S, Felli, V, and Valdinoci, E
- Subjects
Blow-up limit ,Singular weight ,Mathematics::Analysis of PDEs ,Conical geometry ,Boundary (topology) ,01 natural sciences ,010305 fluids & plasmas ,Mathematics - Analysis of PDEs ,Operator (computer programming) ,0103 physical sciences ,FOS: Mathematics ,Neumann boundary condition ,0101 mathematics ,MAT/05 - ANALISI MATEMATICA ,Unique continuation ,Mathematical Physics ,Mathematics ,Forcing (recursion theory) ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Almgren's frequency formula ,Cone (category theory) ,Elliptic curve ,Vertex (curve) ,Gravitational singularity ,Analysis ,Analysis of PDEs (math.AP) - 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.
- Published
- 2020
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