Premium
Equivalence of AMLE, strong AMLE, and comparison with cones in metric measure spaces
Author(s) -
Juutinen Petri,
Shanmugalingam Nageswari
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510411
Subject(s) - mathematics , lipschitz continuity , measure (data warehouse) , metric space , equivalence (formal languages) , mathematical analysis , harmonic function , boundary (topology) , pure mathematics , harmonic measure , null set , metric (unit) , set (abstract data type) , operations management , database , computer science , economics , programming language
In this paper, we study the relationship between p ‐harmonic functions and absolutely minimizing Lipschitz extensions in the setting of a metric measure space ( X, d, μ ). In particular, we show that limits of p ‐harmonic functions (as p → ∞) are necessarily the ∞ ‐energy minimizers among the class of all Lipschitz functions with the same boundary data. Our research is motivated by the observation that while the p ‐harmonic functions in general depend on the underlying measure μ , in many cases their asymptotic limit as p → ∞ turns out have a characterization that is independent of the measure. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)