A priori bounds and necessary conditions for solvability of prescribed curvature equations
An important estimate for the magnitude of solutions of the prescribed higher order mean curvature equations is proven. The results include well known sharp estimates for the mean and Gauss curvature equations. Sharp existence theorems are thus derived for the Dirichlet problem with the aid of already known first and second order derivative estimates. Attention should also be drawn to certain Poincaré and Sobolev type inequalities which are derived as auxiliary results.
scientific article; zbMATH DE number 4152995
scientific article