Equivalent Semi-Norms of Non-Local Dirichlet Forms on the Sierpi\'nski Gasket and Applications
Abstract
We construct equivalent semi-norms of non-local Dirichlet forms on the Sierpi\'nski gasket and apply these semi-norms to a convergence problem and a trace problem. We also construct explicitly a sequence of non-local Dirichlet forms with jumping kernels equivalent to |x-y|-α-β that converges exactly to local Dirichlet form.
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