Abstract: The analysis of elliptic equations on metric spaces has attracted increasing attention over the last two decades. A central problem is the regularity of weak solutions. In this talk I will show that, assuming a lower Ricci curvature bound on the ambient space in a weak sense, it is possible to obtain local Lipschitz regularity of solutions to a general family of quasilinear elliptic equations, including p-harmonic functions. The result is obtained using a Galerkin-type approximation method.
Joint work with S. Schulz.
