### Organiser

#### Seiichiro Kusuoka, Tohoku University

We consider linear parabolic equations of the non-divergence type, and assume the ellipticity and the continuity on the coefficients of the second order derivatives and the boundedness on all the coefficients.  Under the assumptions we show the Hölder continuity of the solution in the spatial component. Furthermore, adding an assumption on the continuity of the coefficient of the second order derivative, we have the Lipschitz continuity of the solution. In the proof, we use a probabilistic method, in particular the coupling method. As a corollary, under an additional assumption we obtain the Hölder and Lipschitz continuity of the fundamental solution in a component.

Name University Dates of visit
Seiichiro Kusuoka Tohoku University 17/02/2015 - 17/02/2015
Total Guests : 1
Name University Dates of visit
Total Guests : 0