Real-valued valuations on Sobolev spaces  

作　　者：MA Dan 

机构地区：[1]Institut für Diskrete Mathematik und Geometrie, Technische Universitat Wien, Wien 1040, Austria

出　　处：《Science China Mathematics》2016年第5期921-934,共14页中国科学：数学（英文版）

基　　金：supported by Austrian Science Fund Project(Grant No.P23639-N18);National Natural Science Foundation of China(Grant No.11371239)

摘　　要：Continuous, SL(n) and translation invariant real-valued valuations on Sobolev spaces are classified.The centro-affine Hadwiger's theorem is applied. In the homogeneous case, these valuations turn out to be L^p-norms raised to p-th power(up to suitable multipication scales).Continuous, SL（n） and translation invariant real-valued valuations on Sobolev spaces are classified.The centro-affine Hadwiger＇s theorem is applied. In the homogeneous case, these valuations turn out to be L^p-norms raised to p-th power（up to suitable multipication scales）.

关 键 词：Sobolev space valuation convex polytope 

分 类 号：O177[理学—数学]