You are here
Visiting Assitant Professor
Heat equation, Dirichlet spaces, heat kernel, heat diffusion
I study the heat equation in Dirichlet spaces. In particular, my research involves heat kernel estimates, and various regularity properties of local weak solutions of the heat equation in Dirichlet spaces that resemble the hypoellipticity of the classical heat operator, under different assumptions on existence of cutoff functions. I also study more concrete examples like the heat diffusion on the infinite dimensional torus.
Rough Hypoellipticity for Local Weak Solutions to the Heat Equation in Dirichlet Spaces. PhD Thesis.