The Cauchy problem for degenerate parabolic equations with discontinuous drift

Conway, Edward D.

doi:10.1090/S0002-9947-1973-0350204-X

The Cauchy problem for degenerate parabolic equations with discontinuous drift
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Trans. Amer. Math. Soc. 179 (1973), 239-249 Request permission

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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