A Lower Bound for the Gradient of infinity-Harmonic Functions

Edi Rosset

Abstract:
We establish a lower bound for the gradient of the solution to infinity-Laplace equation in a strongly star-shaped annulus with capacity type boundary conditions. The proof involves properties of the radial derivative of the solution, so that starshapedness of level sets easily follows.

Submitted November 20, 1995. Published February 6, 1996.
Math Subject Classification: 35J70, 35B05, 35B50,31C45.
Key Words: infinity-harmonic functions, p-harmonic functions.

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Edi Rosset Dipartimento di Scienze Matematiche Universita degli Studi di Trieste 34100 Trieste, Italy e-mail: rossedi@univ.trieste.it

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