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

DOI:
https://doi.org/10.1090/S0002-9947-1973-0350204-X

MathSciNet review:
0350204

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1973-0350204-X

Keywords:
Degenerate parabolic equation,
discontinuous coefficients,
diffusion processes,
stochastic differential equations

Article copyright:
© Copyright 1973
American Mathematical Society