月曜解析セミナー: Intrinsic ultracontractivity and the boundary Harnack principle — A unified approach with capacitary width

開催日時
2013年   4月 15日 14時 45分 ~ 2013年   4月 15日 16時 15分
場所
理学部3号館210
講演者
相川 弘明(北海道大学)
 
We study intrinsic ultracontractivity (IU) for the semigroup associated with Dirichlet heat kernel. We give a sharp sufficient condition for IU, valid for arbitrary domains, in terms of capacitary width of sublevel sets of the Green function and the ground state. This condition, together with the Harnack inequality, yields more specific sufficient conditions for IU of nonsmooth domains.  Our approach employs a parabolic box argument, a counterpart of the box argument for the boundary Harnack principle. We can treat IU and the boundary Harnack principle in parallel.
Our method is purely analytic and elementary; it enables us to dispense with logarithmic Sobolev inequalities.

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研究集会・セミナー・集中講義の一覧へ