The nonhomogeneous minimal surface equation involving a measure
We find existence of a minimum in BV for the variational problem associated with \(\text{div } A(Du)+ \mu= 0\), where \(A\) is a mean curvature type operator and \(\mu\) a nonnegative measure satisfying a suitable growth condition. We then show a local \(L^ \infty\) estimate for the minimum. A similar local \(L^ \infty\) estimate is shown for sub- solutions that are Sobolev rather than BV.
nonlinear elliptic partial differential equations
scientific article; zbMATH DE number 759258