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Regularity of locally convex surfaces

Published online by Cambridge University Press:  17 April 2009

Friedmar Schulz
Friedmar Schulz
Affiliation:
Department of Mathematics, The University of Iowa, Iowa City, IA 52242, United States of America Centre for Mathematical Analysis, The Australian National University, GPO Box 4, Canberra ACT 2601, Australia
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Abstract

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Interior estimates are derived for the C2, µ-Hölder norm of the radius vector X ∈ C1, 1 (Ω) of a locally convex surface Σ in terms of the first fundamental form IΣ, the Gauss curvature K and the integral ∫ |H| dσ. Here H is the mean curvature of Σ. The coefficients gij of IΣ are assumed to belong to the Hölder class C2, µ (Ω) for some μ, 0 < μ < 1. A boundary condition is discussed which ensures an estimate for ∫ | H | dσ.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 3 , December 1990 , pp. 487 - 497
Copyright
Copyright © Australian Mathematical Society 1990

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