Abstract
We describe singular diffusion in bounded subsets \({\Omega}\) of \({\mathbb{R}^{n}}\) by form methods and characterize the associated operator. We also prove positivity and contractivity of the corresponding semigroup. This results in a description of a stochastic process moving according to classical diffusion in one part of \({\Omega}\), where jumps are allowed through the rest of \({\Omega}\).
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Freiberg, U., Seifert, C. Dirichlet forms for singular diffusion in higher dimensions. J. Evol. Equ. 15, 869–878 (2015). https://doi.org/10.1007/s00028-015-0284-4
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DOI: https://doi.org/10.1007/s00028-015-0284-4