Dirichlet spaces and boundary conditions for submarkovian resolvents

Absorption semigroups and dirichlet boundary conditions

Resolvents of self-adjoint extensions with mixed boundary conditions

We prove a variant of Krein’s resolvent formula for self-adjoint extensions given by arbitrary boundary conditions. A parametrization of all such extensions is suggested with the help of two bounded operators instead of multivalued operators and selfadjoint linear relations.

TECHNISCHE UNIVERSITÄT BERLIN Moving Dirichlet Boundary Conditions

This paper develops a framework to include Dirichlet boundary conditions on a subset of the boundary which depends on time. In this model, the boundary conditions are weakly enforced with the help of a Lagrange multiplier method. In order to avoid that the ansatz space of the Lagrange multiplier depends on time, a bi-Lipschitz transformation, which maps a fixed interval onto the Dirichlet bound...

Quasi-regular topologies for L-resolvents and semi-Dirichlet forms

We prove that for any semi-Dirichlet form (ε, D(ε)) on a measurable Lusin space E there exists a Lusin topology with the given σ-algebra as the Borel σ-algebra so that (ε, D(ε)) becomes quasi–regular. However one has to enlarge E by a zero set. More generally a corresponding result for arbitrary L-resolvents is proven.

Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions

when ε ≥ 0 is small. In particular, ∆2v + εv ≥ 0 in Ω, with v = ∆v = 0 on ∂Ω, implies v ≥ 0 for ε small. In numerical experiments ([14]) for one dimension a similar behaviour was observed under Dirichlet boundary conditions v = ∂ ∂nv = 0. In this paper we will derive a 3-G type theorem as in (1) but with G1,n replaced by the Green function Gm,n for the m-polyharmonic operator with Dirichlet bou...