F. Roodenburg

Optimal semigroup estimates and functional calculus for the Laplacian on weighted Sobolev spaces

In this paper, we consider the Laplace operator on the half-space with Dirichlet and Neumann boundary conditions. These operators are studied on Sobolev spaces with power weights measuring the distance to the boundary. We prove optimal estimates for the resolvent operators and the corresponding heat semigroups. In addi...