Abstract: In this talk I will first recall the equivalence between ∞-harmonic functions and the absolute minimizers of the L∞-variational problem for the Hamiltonian H(x,p)=|p|^2, and also some regularity results of ∞-harmonic functions obtained by Savin, Evans and Smart. Then we consider the L∞-variational problem for the Hamiltonian H(x,p)=, where A is uniform elliptic. If A is also C^{1,1}, based the ideas of Evans-Smart and using the intrinsic (Riemannian) distance determined by A, we obtained the differentiability everywhere of the absolute minimizer of such L∞-variational problems. Finally, several open problems for L∞-variational problems will be listed.

Time: 10:10am-12:00pm, Tuesday, April 07

Place: Room 29, Quan Zhai, BICMR

Speaker: Professor ZHOU Yuan, BUAA