A convergence theorem for Dirichlet forms with applications to boundary value problems with varying domains.
A dual characterization of length spaces with application to Dirichlet metric spaces
We show that under minimal assumptions, the intrinsic metric induced by a strongly local Dirichlet form induces a length space. The main input is a dual characterization of length spaces in terms of the property that the 1-Lipschitz functions form a sheaf.
Representation of operators by kernels.
We prove that differences of order-continuous operators acting between function spaces can be represented with a pseudo-kernel, proved the underlying measure spaces satisfy certain (rather weak) conditions. To see that part of these conditions are necessary, we show that the strict localizability of a measure space can be characterized by the existence of a pseudo-kernel for a certain operator.
The Allegretto-Piepenbrink theorem for strongly local Dirichlet forms.
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