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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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Construction of Elliptic Diffusions,g Feller process solves the martingale problem for the .-generator for every starting point where the drift is not singular and that is either in the interior of the domain or at a ..-smooth boundary point.
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Construction of the Local Time and Skorokhod Decomposition,For this we first need to refine a construction result for additive functionals of Fukushima, Oshima and Takeda ([FOT11]) to our setting, see Theorem 6.1.11. The construction of the local time is based on boundedness properties of the corresponding potential that are proven using our elliptic regularity result of Chapter 3.1, see Theorem 6.2.1.
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Bo Jiang,Yuan Liu,Hao Zhang,Xuehou Tanrong Feller process associated with gradient Dirichlet forms. This is done in the next two sections. We apply the regularity result from Chapter 3 to prove local Hölder continuity of the .-resolvent for specified .. We postpone the proof to Section 4.2. It is applied only in Theorem 4.1.9. Furthermo
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