Monday Analysis Seminar: Principlal frequency of an arbitrary domain and Intrinsic Ultracontractivity of the heat kernel

Date
2016-12-19 14:45 - 2016-12-19 16:15
Place
Faculty of Science Building #3 Room 205
Speaker/Organizer
Hiroaki Aikawa (Hokkaido University)
 
We estimate the principal frequency of an arbitrary domain in terms of capacitary width. Sharp sufficient conditions for Intrinsic Ultracontractivity (IU) of the heat kernel and the Global Boundary Harnack principle are given by integral conditions of capacitary width of the level set of the Green function. Since IU is regarded as a parabolic boundary Harnack principle, our method leads to a unified treatment for parabolic and elliptic boundary Harnack principles.