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.

冒失

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