## A lower bound for the gradient of $\infty$-harmonic functions

### Summary

Summary: 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.

### Mathematics Subject Classification

35J70, 35B05, 35B50, 31C45

### Keywords/Phrases

infinity-harmonic functions, p-harmonic functions