$C^{1,\alpha}$ regularity for the parabolic homogeneous pLaplacian equation
$C^{1,\alpha}$ regularity for the parabolic homogeneous pLaplacian equation

Luis Silvestre, University of Chicago
Fine Hall 314
It is well known that pharmonic functions are $C^{1,\alpha}$ regular, for some $\alpha>0$. The classical proofs of this fact uses variational methods. In a recent work, Peres and Sheffield construct pHarmonic functions from the value of a stochastic game. This construction also leads to a parabolic versions of the problem. However, the parabolic equation derived from the stochastic game is not the classical parabolic pLaplace equation, but a homogeneous version. This equation is not in divergence form and variational methods are inapplicable. We prove that solutions to this equation are also $C^{1,\alpha}$ regular in space. This is joint work with Tianling Jin.