Thalia Jeffres
Universidad Michoacana
Regularity of the Heat Operator on a Cone
Abstract: In this joint work with Paul Loya, we study differentiability properties of solutions to heat equation on a cone manifold. The heat operator considered here is that which corresponds to the Friedrichs extension of the Laplacian. For initial data in appropriately defined H\"{o}lder spaces, the estimates are good enough to prove existence of solutions of certain semilinear parabolic equations.