Regularity of Fractional Heat Semigroup Associated with Schrödinger Operators
Regularity of Fractional Heat Semigroup Associated with Schrödinger Operators
Let L=−Δ+V be a Schrödinger operator, where the potential V belongs to the reverse Hölder class. By the subordinative formula, we introduce the fractional heat semigroup {e−tLα}t>0, 0<α<1, associated with L. By the aid of the fundamental solution of the heat equation: ∂tu+Lu=∂tu−Δu+Vu=0, we estimate the gradient and the time-fractional …