月曜解析セミナー： Global integrability of supertemperatures

開催日時

2018年5月21日 15時00分 ～ 2018年5月21日 16時30分

場所

理学部3号館202

講演者

相川 弘明（北海道大学）

Ever since Armitage showed that every nonnegative superharmonic function on a bounded domain of bounded curvature ( domain) in is -integrable up to the boundary for , the global integrability of nonnegative supersolutions has attracted many mathematicians.

In this talk we consider a parabolic counterpart. We study the global integrability of nonnegative supertemperatures on the cylinder , where is a Lipschitz domain or a John domain. We show that the integrability depends on the lower estimate of the Green function for the Dirichlet Laplacian on . In particular, if is a bounded -domain, then every nonnegative supertemperature on is -integrable over for any , provided . The bound is sharp.

Joint work with Hara and Hirata.