Dirichlet forms for singular diffusion in higher dimensions

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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Correspondence to Christian Seifert.

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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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Mathematics Subject Classification

  • 47D06
  • 47A07
  • 35Hxx
  • 35J70
  • 60J45

Keywords

  • Singular diffusion
  • Dirichlet forms
  • Submarkovian semigroups
  • Jump-diffusion process