Titlebook: Elliptic Boundary Value Problems and Construction of Lp-Strong Feller Processes with Singular Drift ; Benedict Baur Book 2014 Springer Fac

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Mathematical Problems and ProofsThe aim of this chapter is to prove a Sobolev space regularity result for weak solutions of elliptic equations. This result will be used for the construction of .-strong Feller processes in the next chapter. It will be also used for the construction of the boundary local time.

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Introduction,This thesis consists of three main parts: First, the construction of .-strong Feller processes from sub-Markovian strongly continuous contraction semigroups on .-spaces that are associated with symmetric regular Dirichlet forms, see Chapter 2.

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Elliptic Regularity up to the Boundary,The aim of this chapter is to prove a Sobolev space regularity result for weak solutions of elliptic equations. This result will be used for the construction of .-strong Feller processes in the next chapter. It will be also used for the construction of the boundary local time.

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Appendix,In this section we consider some useful results concerning locally compact separable metric spaces with a locally finite Borel measure .. Let (., d) be a metric space. We say that . is . if for every . ∈ . there exists an open neighborhood . of . such that . is compact.

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https://doi.org/10.1007/978-3-658-05829-6Dirichlet form theory; Skorokhod decomposition; elliptic boundary value problem; finite particle system

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978-3-658-05828-9Springer Fachmedien Wiesbaden 2014