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On the existence of Feller semigroups with discontinuous coefficients. II. (English) Zbl 1175.47041

Summary: This paper is devoted to the functional analytic approach to the problem of existence of Markov processes with Dirichlet boundary condition, oblique derivative boundary condition and first-order Wentzell boundary condition for second-order, uniformly elliptic differential operators with discontinuous coefficients. More precisely, we construct Feller semigroups associated with absorption, reflection, drift and sticking phenomena at the boundary. The approach here is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the Calderón–Zygmund theory of singular integral operators with non-smooth kernels.
[For Part I, see Acta Math.Sin., Engl.Ser.22, No.2, 595–606 (2006; Zbl 1113.47030).]

MSC:

47D07 Markov semigroups and applications to diffusion processes
35J25 Boundary value problems for second-order elliptic equations
60J35 Transition functions, generators and resolvents
60J60 Diffusion processes

Citations:

Zbl 1113.47030
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References:

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