The nonhomogeneous minimal surface equation involving a measure
William P. Ziemer · Pacific Journal of Mathematics · 1995
We find existence of a minimum in BV for the variational problem associated with div A{Du) + μ = 0, where A is a mean curvature type operator and μ a nonnegative measure satisfying a suitable growth condition.We then show a local L°° estimate for the minimum.A similar local L°° estimate is shown for sub-solutions that are Sobolev rather than BV.