Abstract
Dirichlet forms are various generalizations of the classical Dirichlet integral
where Ω is a domain in ℝn, f∈C ∞0 (ℝn). The relation between the above Dirichlet integral, the solution of the Dirichlet problem for the Laplacian on Ω, “stopped” Brownian motion, and the associated heat equation (and its semigroup) has long been known. We refer to Fukushima (1980) and Silverstein (1974) for systematic, self-contained expositions, and for comprehensive references.
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© 1993 Springer Science+Business Media Dordrecht
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Hida, T., Kuo, HH., Potthoff, J., Streit, L. (1993). Dirichlet Forms. In: White Noise. Mathematics and Its Applications, vol 253. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3680-0_10
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DOI: https://doi.org/10.1007/978-94-017-3680-0_10
Publisher Name: Springer, Dordrecht
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