Everywhere differentiability of infinity harmonic functions

We show that an infinity harmonic function, that is, a viscosity solution of the nonlinear PDE , is everywhere differentiable. Our new innovation is proving the uniqueness of appropriately rescaled blow-up limits around an arbitrary point.

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2011-09, Vol.42 (1-2), p.289-299
Main Authors: Evans, Lawrence C., Smart, Charles K.
Format: Article
Language:English
Subjects:
Analysis
Calculus
Calculus of variations
Calculus of Variations and Optimal Control
Optimization
Control
Harmonic functions
Infinity
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Nonlinearity
Partial differential equations
Systems Theory
Theoretical
Uniqueness
Viscosity
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Description
Summary:We show that an infinity harmonic function, that is, a viscosity solution of the nonlinear PDE , is everywhere differentiable. Our new innovation is proving the uniqueness of appropriately rescaled blow-up limits around an arbitrary point.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-010-0388-1