Abstract
The aim of this chapter is to develop in the context of obstacles (i.e. V ≥ 0), the notions of potential theory, we shall later use. In Section 2 we collect some results on Green functions. In Section 3 we introduce, à la Chung, equilibrium potentials, equilibrium distributions and capacities by means of last exit distributions. Section 4 develops the maximum principle, the variational principle as well as a number of examples. In Section 5 we link capacity and Dirichlet forms, through another variational formula.
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Notes and References
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© 1998 Springer-Verlag Berlin Heidelberg
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Sznitman, AS. (1998). Some Potential Theory. In: Brownian Motion, Obstacles and Random Media. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11281-6_2
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DOI: https://doi.org/10.1007/978-3-662-11281-6_2
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