We first review recent results on the regularity of solutions to equations driven by non-local operators. The main emphasis is then on integro-differential operators of fractional order with a jump measure that is singular with respect to the d-dimensional Lebesgue measure. The corresponding Dirichlet form generates a Markov process of d independent copies of one-dimensional jump processes. As a main result, we prove sharp two-sided bounds of the fundamental solution and Hölder-regularity for solutions to eliptic and parabolic problems. The talk is based on recent joint results together with (a) B. Dyda, (b) J. Chaker and (c) K. Kim, T. Kumagai.
Donnerstag, den 5. Dezember 2019 um 17.15 Uhr, in INF 205, HS Mathematikon Donnerstag, den 5. Dezember 2019 at 17.15, in INF 205, HS Mathematikon
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Hans Knüpfer