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Einige Bemerkungen über die Regularität von stationären Punkten gewisser geometrischer Variationsintegrale
Author(s) -
Duzaar Frank,
Fuchs Martin
Publication year - 1991
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.19911520105
Subject(s) - mathematics , isoperimetric inequality , conformal map , degenerate energy levels , pure mathematics , ball (mathematics) , geometry , physics , quantum mechanics
We discuss the regularity properties of weak solutions of certain degenerate elliptic systems arising from problems in geometry. For example we prove C 1 ‐regularity of conformal m ‐harmonic maps from the m ‐ball into m ‐dimensional oriented submanifolds of R m+1 as well as a regularity theorem for weak H ‐surfaces in R m+1 . Our arguments make strong use of a version of the isoperimetric inequality.