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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The Cauchy problem for degenerate parabolic equations with discontinuous drift

Author: Edward D. Conway
Journal: Trans. Amer. Math. Soc. 179 (1973), 239-249
MSC: Primary 35K15
MathSciNet review: 0350204
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Abstract: The coefficient of the gradient is allowed to be discontinuous but is assumed to satisfy a ``one-sided'' Lipschitz condition. This condition insures the pathwise uniqueness of the underlying Markov process which in turn yields the existence of a unique stable generalized solution of the parabolic equation. If the data is Lipschitz continuous, then so is the solution.

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Keywords: Degenerate parabolic equation, discontinuous coefficients, diffusion processes, stochastic differential equations
Article copyright: © Copyright 1973 American Mathematical Society