Doubly Feller Property of Brownian Motions with Robin Boundary Condition

Abstract

In this paper, we consider first order Sobolev spaces with Robin boundary condition on unbounded Lipschitz domains. Hunt processes are associated with these spaces. We prove that the semigroup of these processes are doubly Feller. As a corollary, we provide a condition for semigroups generated by these processes being compact.

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Acknowledgments

The author would like to thank Professor Masayoshi Takeda for detailed discussions and helpful support. He would like to thank referees for their valuable comments and suggestions which improve the quality of the paper. He would also like to thank Dr. Masaki Wada for encouragement.

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Correspondence to Kouhei Matsuura.

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Matsuura, K. Doubly Feller Property of Brownian Motions with Robin Boundary Condition. Potential Anal 53, 23–53 (2020). https://doi.org/10.1007/s11118-018-09758-4

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Keywords

  • Boundary local time
  • Dirichlet form
  • Extension domain
  • Robin boundary condition

Mathematics Subject Classification (2010)

  • 31C15
  • 31C25
  • 60J60
  • 47D08