Differential and Integral Equations

Some observations on the local behaviour of infinity-harmonic functions

Tilak Bhattacharya

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Abstract

We study some aspects of the local behaviour of infinity-harmonic functions. We study one-sided radial derivatives at points of extrema on the boundary of concentric balls and relate it to some issues in differentiability. In particular we show differentiability of these functions at such points of extrema. We use convexity and the Harnack inequality to obtain our results.

Article information

Source
Differential Integral Equations, Volume 19, Number 8 (2006), 945-960.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050342

Mathematical Reviews number (MathSciNet)
MR2263436

Zentralblatt MATH identifier
1212.35163

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15] 31C05: Harmonic, subharmonic, superharmonic functions 35J70: Degenerate elliptic equations

Citation

Bhattacharya, Tilak. Some observations on the local behaviour of infinity-harmonic functions. Differential Integral Equations 19 (2006), no. 8, 945--960. https://projecteuclid.org/euclid.die/1356050342


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