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Transactions of the American Mathematical Society

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Solving semilinear partial differential equations with probabilistic potential theory


Authors: Joseph Glover and P. J. McKenna
Journal: Trans. Amer. Math. Soc. 290 (1985), 665-681
MSC: Primary 35J60; Secondary 35K55, 60J45
MathSciNet review: 792818
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Abstract: Techniques of probabilistic potential theory are applied to solve $ - Lu + f(u) = \mu $, where $ \mu $ is a signed measure, $ f$ a (possibly discontinuous) function and $ L$ a second order elliptic or parabolic operator on $ {R^d}$ or, more generally, the infinitesimal generator of a Markov process. Also formulated are sufficient conditions guaranteeing existence of a solution to a countably infinite system of such equations.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0792818-7
Article copyright: © Copyright 1985 American Mathematical Society