Local regularity and p-harmonic approximation for weak inverse mean curvature flow
We prove local Lipschitz regularity for locally bounded solutions of the calibration equations for inverse mean curvature flow. We also approximate every prescribed variational weak flow locally by Moser's logarithmic transforms of positive -harmonic functions. On a fixed smooth domain, with the trace of a calibrated Lipschitz solution prescribed, both the uniform error and the absolute difference of total variations are as . In particular, the approximations converge strictly in .