Unique continuation principles in cones under nonzero Neumann boundary conditions
Analysis of PDEs
2019-03-28 v1
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.
Cite
@article{arxiv.1903.11520,
title = {Unique continuation principles in cones under nonzero Neumann boundary conditions},
author = {Serena Dipierro and Veronica Felli and Enrico Valdinoci},
journal= {arXiv preprint arXiv:1903.11520},
year = {2019}
}