Marianna Porfido on “General kernel estimates of Schrödinger type operators with unbounded diffusion terms”

In this talk we consider a Schrödinger type operator A with
unbounded diffusion coefficients. We first prove that a
realization of A in L^2(R^d) generates a sub-Markov and ultracontractive semigroup on L^2(R^d). Second, using time dependent Lyapunov functions, we show pointwise upper
bounds for the heat kernel and we apply the results in case of
polynomially and exponentially diffusion and potential coefficients.

A joint work with Loredana Caso (Univ. Salerno), Markus Kunze (Univ. Konstanz), Abdelaziz Rhandi (Univ. Salerno)