Time : 2021/8/12 Thu 16:00~17:00
Location : Online (ZOOM) https://us02web.zoom.us/j/81369983747?pwd=SUpVK0ZUalFxY0JmU2xOMnBCVGFBdz09
Speaker : 박대한 (SAARC, KAIST)
Title : On the Lq(Lp)-theory for diffusion equations with space-time non-local operators
Abstract: Various kinds of non-local operators are used to describe many physical models. For example the relativistic correction of kinetic energy is a non-local operator which is used to find the fine structure of the energy level for the hydrogen atom. Also, it turns out that many non-local operators can be understand as the infinitesimal generator of some stochastic processes. A well-known example of such relation can be found in the fractional Laplacian which is the infinitesimal generator of -stable process.
In this talk, we will consider equations with space-time non-local operators , where is the Caputo fractional derivative of order . The spatial operator is a composition of Laplacian and Bernstein function which is the infinitesimal generator of a subordinate Brownian motion. We derive the estimation of the fundamental solution to our equation by using estimates of parabolic heat kernel of subordinate Brownian motion and by using this we will show Lq(Lp) estimation of solution.