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arXiv · 0804.4519

Cordes conditions and some alternatives for parabolic equations and discontinuous diffusion

Nikolai Dokuchaev
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Abstract

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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Nikolai Dokuchaev. 2008-04-29. Cordes conditions and some alternatives for parabolic equations and discontinuous diffusion. https://arxiv.org/abs/0804.4519

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