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Acta Mathematicae Applicatae Sinica

, Volume 6, Issue 2, pp 126–134 | Cite as

Probabilistic approach to the Neumann problem

  • Zhang Tusheng 
Article

Abstract

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.

Keywords

Weak Solution Local Time Explicit Formula Neumann Boundary Probabilistic Approach 
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References

  1. [1]
    Pei Hsu, Probabilistic Approach to the Neumann Problem.Comm. Pure Appl. Math.,38: 4(1985), 444–472.Google Scholar
  2. [2]
    Ph. Blanchard, Zhiming Ma, Semigroup of Schrodinger Operators with Potentials Given by Radon Measure, BiBos Preprint, No. 262, 1987.Google Scholar
  3. [3]
    M. Fukushima, Dirichlet Forms and Markov Processes, North-Holland Publ. Co. and Kodansha, 1980.Google Scholar
  4. [4]
    Pei Hsu, Reflecting Brownian Motion, Boundary Local Time and the Neumenn Problem, Ph. D. Dissertations, Stanford University, 1984.Google Scholar
  5. [5]
    Zhang Tusheng, The Characterization of Local Time ofd-dimensional Brownian Motion and Representation Theorems of Additive Functional,Acta Mathematica Sinica (in Chinese),32, 2 (1989), 161–173.Google Scholar

Copyright information

© Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A. 1990

Authors and Affiliations

  • Zhang Tusheng 
    • 1
  1. 1.Institute of Applied, MathematicsAcademia SinicaChina

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