Nikolai Dokuchaev
Published 2008-04-29Version 1
The paper considers parabolic equations in non-divergent form with discontinuous coefficients at higher derivatives. Their investigation is most complicated because, in general, in the case of discontinuous coefficients, the uniqueness of a solution for nonlinear parabolic or elliptic equations can fail, and there is no a priory estimate for partial derivatives of a solution. In this paper, existence and regularity results are obtained under some Cordes type restrictions on the coefficients. The results are applied to diffusion processes.
Comments: 18 pages
Journal: Differential equations 33 (4), English translation: 1997, pp. 433-442, in Russian: 1996, pp. 552-531
Parabolic equations with measurable coefficients in $L_p$-spaces with mixed norms
Recent progress in the $L_p$ theory for elliptic and parabolic equations with discontinuous coefficients
On linear elliptic and parabolic equations with growing drift in Sobolev spaces without weights
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