An energy estimate for the difference of solutions for the n-dimensional equation with prescribed mean curvature and removable singularities
Stefan Hildebrandt, Friedrich Sauvigny · Analysis · 2009
We derive an energy bound, estimating a weighted Dirichlet integral of two solutions for the nonparametric equation with prescribed mean curvature in n dimensions in terms of the L 1 -norm for the difference of their values on the boundary. Furthermore, a similar estimate is established for solutions of the equation div F p (·,∇ u )= n H (·, u ), where F(x,p) denotes an elliptic Lagrangian with linear growth in p . These results are used to remove singularities of solutions to these equations.