Paolo Albano

Unique continuation for second-order parabolic operators at the initial time

We consider second-order parabolic equations with time independent coefficients. Under reasonable assumptions, it is known that the fundamental solution satisfies certain Gaussian bounds related to the associated geodesic distance. In this article we prove a sharp unique continuation property at the initial time which matches exactly the above-mentioned kernel bounds.

Singular gradient flow of the distance function and homotopy equivalence

Let

Singularities of Semiconcave Functions in Banach Spaces

M

Analytic stratifications and the cut locus of a class of distance functions

be a Riemannian manifold and let

On the Eikonal equation for degenerate elliptic operators

\varOmega

On the singular set for solutions to a class of Hamilton-Jacobi-Bellman equations

be a bounded open subset of