Regularity properties for time fractional heat equation
芬兰Helsinki(赫尔辛基)大学数学系 摘要:Non-local integro-differential equations have attained a lot of attention in physical applications during the last decade. Consequently, also the mathematical theory has gathered a lot of attention and especially the fractional laplacian and its parabolic versions have been studied extensively. In this mini-course we will study a different version of non-local heat diffusion, where the fractional operator is in time instead of space. This kind of equations arise, for instance, in statistical physics as a random walk model for anomalous diffusion. We will concentrate on the mathematical regularity theory of weak solutions and, in particular, we will prove the parabolic Harnack inequality for such equations. If time permits, we will also study H?lder regularity as well as some new decay results for the solutions. The talks are arranged as self-contained as possible and are suitable also for graduate students.