Spectral Gap for Stable Process on Convex Planar Double Symmetric Domains |
| |
Authors: | Bartłomiej Dyda Tadeusz Kulczycki |
| |
Affiliation: | (1) Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland |
| |
Abstract: | We study the semigroup of the symmetric α-stable process in bounded domains in R 2. We obtain a variational formula for the spectral gap, i.e. the difference between two first eigenvalues of the generator of this semigroup. This variational formula allows us to obtain lower bound estimates of the spectral gap for convex planar domains which are symmetric with respect to both coordinate axes. For rectangles, using “midconcavity” of the first eigenfunction (Bañuelos et al., Potential Anal. 24(3): 205–221, 2006), we obtain sharp upper and lower bound estimates of the spectral gap. |
| |
Keywords: | Symmetric stable process Spectral gap Convex domain |
本文献已被 SpringerLink 等数据库收录! |
|