On applications of the Levi method in the theory of parabolic equations
Journal Title: Математичні Студії - Year 2017, Vol 47, Issue 1
Abstract
A short review of papers where a fundamental solution was constructed by the Levi’s parametrix method is done. Some details of applications of this method for parabolic equations and systems of parabolic equations, in particular the procedure of constructing a parametrix for equations with different degenerations and singularities, are considered. The basic results of constructing of a fundamental solution for degenerate ultraparabolic equations of the Kolmogorov type by the Levi paramerix method under different assumptions on the coefficients are reviewed. Some new authors’ results on the constructing of a classical fundamental solution and, so-called, L-fundamental solution for the equation with coefficients with two groups of spatial variables are presented. These results are obtained by stepwise using of the Levi parametrix method and special Holder conditions on the coefficients.
Authors and Affiliations
S. D. Ivasyshen, I. P. Medynsky
Keywords
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- EP ID EP310039
- DOI 10.15330/ms.47.1.33-46
- Views 55
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