Cordes conditions and some alternatives for parabolic equations and discontinuous diffusion

Details Cordes conditions and some alternatives for parabolic equations and discontinuous diffusion Cordes conditions and some alternatives for parabolic equations and discontinuous diffusion

2008-04-29

arxiv.org/abs/0804.4519v1

Differential equations 33 (4), English translation: 1997, pp. 433-442, in Russian: 1996, pp. 552-531

Mathematics

Analysis of PDEs

18 pages

Scientific paper

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.

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