Schroedinger operators on exterior domains with Robin boundary conditions: heat kernel estimates

Abstract

We study Schroedinger operators with Robin boundary conditions on exterior domains in ${\mathbb{R}}^d$. We prove sharp point-wise estimates for the associated semi-groups which show, in particular, how the boundary conditions affect the time decay of the heat kernel in dimensions one and two. Applications to spectral estimates are discussed as well.

References in corpus (1)

• Large time behavior of the heat kernel of two-dimensional magnetic Schroedinger operators

Cited by in corpus (3)

• Global well-posedness, dissipation and blow up for semilinear heat equations in energy spaces associated with self-adjoint operators
• Global existence and asymptotic behavior for semilinear damped wave equations on measure spaces
• Bounds and Gaps of Positive Eigenvalues of Magnetic Schrödinger Operators with No or Robin Boundary Conditions