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.
Dipierro, S., Felli, V., Valdinoci, E. (2020). Unique continuation principles in cones under nonzero Neumann boundary conditions. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 37(4), 785-815 [10.1016/j.anihpc.2020.01.005].
Unique continuation principles in cones under nonzero Neumann boundary conditions
Felli V.;
2020
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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