Probabilistic approach to the Neumann problem
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In this paper, we consider the Neumann boundary value problem of Schrödinger operator with measure potential μ. First, a martingale formulation of the Neumann problem and an analytic characterization of the martingale formulation are given. Then, by using the Dirichlet forms and Stochastic analysis we obtain an explicit formula for the unique weak solution of this problem in terms of reflecting Brownias motion and it's boundary local time.
KeywordsWeak Solution Local Time Explicit Formula Neumann Boundary Probabilistic Approach
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