On the existence and regularity of hypersurfaces of prescribed Gauss curvature with boundary Bo Guan Indiana University Mathematics Journal 1995 text pdf 10.1512/iumj.1995.44.1985 10.1512/iumj.1995.44.1985 en Indiana Univ. Math. J. 44 (1995) 221 - 242 state-of-the-art mathematics http://iumj.org/access/