The Laplacian with nonlocal Robin boundary conditions.

摘要

This dissertation deals with the realization of the Laplacian with nonlocal Robin boundary conditions on various domains. We investigate the well-posedness of the boundary value problem with nonlocal Robin boundary conditions on different kinds of bounded domains, and prove existence and regularity of weak solutions associated with the nonlocal Robin boundary value problem. The regularity of the weak solutions improve as the domain becomes more regular. Then, we define the nonlocal Robin Laplacian, and obtain results about generation of strongly continuous semigroups associated with the Laplace operator with nonlocal boundary conditions.