866 research outputs found
Energy measure closability for Dirichlet forms
We consider symmetric Dirichlet forms on locally compact and non-locally
compact spaces and provide an elementary proof for their closability with
respect to energy dominant measures. We also discuss how to use known potential
theoretic results to furnish an alternative proof of this theorem
Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces
Starting with a regular symmetric Dirichlet form on a locally compact
separable metric space , our paper studies elements of vector analysis,
-spaces of vector fields and related Sobolev spaces. These tools are then
employed to obtain existence and uniqueness results for some quasilinear
elliptic PDE and SPDE in variational form on by standard methods. For many
of our results locality is not assumed, but most interesting applications
involve local regular Dirichlet forms on fractal spaces such as nested fractals
and Sierpinski carpets
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