Speaker
Alessandra de Luca, Università degli Studi di Milano Bicocca
Abstract
I will discuss the validity of the strong unique continuation property at the boundary for solutions to a class of nonlocal elliptic equations driven by the spectral fractional Laplacian. More precisely, an extension procedure allows to reduce the problem to a local one in one dimension more, posed on a cylinder with a homogeneous Dirichlet condition on the lateral boundary and a non-homogeneous Neumann condition on the base. For the extended problem, after an odd reflection across the junction between the base and the lateral boundary of the cylinder, enough regularity is available to derive a Pohozaev-type identity and consequently some doubling properties via an Almgren-type monotonicity formula. Combining this with a blow-up analysis, we get information on all the admissible vanishing orders of solutions, and hence the validity of the strong unique continuation property for the nonlocal problem.
Alessandra de Luca, Università degli Studi di Milano Bicocca
Abstract
I will discuss the validity of the strong unique continuation property at the boundary for solutions to a class of nonlocal elliptic equations driven by the spectral fractional Laplacian. More precisely, an extension procedure allows to reduce the problem to a local one in one dimension more, posed on a cylinder with a homogeneous Dirichlet condition on the lateral boundary and a non-homogeneous Neumann condition on the base. For the extended problem, after an odd reflection across the junction between the base and the lateral boundary of the cylinder, enough regularity is available to derive a Pohozaev-type identity and consequently some doubling properties via an Almgren-type monotonicity formula. Combining this with a blow-up analysis, we get information on all the admissible vanishing orders of solutions, and hence the validity of the strong unique continuation property for the nonlocal problem.