Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-1973-0350204-X
MathSciNet review: 0350204
Full-text PDF

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35K15

Retrieve articles in all journals with MSC: 35K15


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

American Mathematical Society