月曜解析セミナー: Extended Harnack inequalities with exceptional sets and a boundary Harnack principle

開催日時
2012年   4月 9日 14時 45分 ~ 2012年   4月 9日 16時 15分
場所
北海道大学理学部3号館210
講演者
相川 弘明(北海道大学理学研究院)
 
The Harnack inequality is one of the most fundamental inequalities for positive harmonic functions and, it is extended for positive solutions to general elliptic equations and parabolic equations.  This talk gives a different view point of generalization.  We generalize Harnack chains rather than equations.  More precisely, we introduce a Harnack double chain in association with quasihyperbolic metric and allow a small exceptional set; and yet we obtain a similar Harnack inequality.  The size of an exceptional set is measured by capacity.  The results are new even for classical harmonic functions.

Our extended Harnack inequality involves information for the boundary behavior of positive harmonic functions.  It yields a boundary Harnack principle for a very nasty domain whose boundary is given locally by the graph of a function with modulus of continuity worse than Hölder continuity.

関連項目

研究集会・セミナー・集中講義の一覧へ