Solving semilinear partial differential equations with probabilistic potential theory

Glover, Joseph; McKenna, P. J.

doi:10.1090/S0002-9947-1985-0792818-7

Solving semilinear partial differential equations with probabilistic potential theory
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by Joseph Glover and P. J. McKenna PDF

Trans. Amer. Math. Soc. 290 (1985), 665-681 Request permission

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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Differential inequalities