Everywhere differentiability of infinity harmonic functions

By Lawrence C. Evans, Charles K. Smart. 2011

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We show that an infinity harmonic function, that is, a viscosity solution of the nonlinear PDE $${- \Delta_\infty u = -u_{x_i}u_{x_j}u_{x_ix_j} = 0}$$, is everywhere differentiable. Our new innovation is proving the uniqueness of appropriately rescaled blow-up limits around an arbitrary point.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/6025b34f939a7bded2843fe410eb31cf855f2463