On second derivative estimates for equations of Monge-Ampère type
- 1 December 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 30 (3) , 321-334
- https://doi.org/10.1017/s0004972700002069
Abstract
We derive interior second derivative estimates for solutions of equations of Monge-Ampère type which extend those of Pogorelov for the case of affine boundary values. A key ingredient in our method is the existence of a strong solution of the homogeneous Monge-Ampère equation.Keywords
This publication has 7 references indexed in Scilit:
- Elliptic Partial Differential Equations of Second OrderPublished by Springer Nature ,2001
- Classical solvability of the Dirichlet problem for the Monge-Ampère equationJournal of Mathematical Sciences, 1985
- The dirichlet problem for nonlinear second‐order elliptic equations I. Monge‐ampégre equationCommunications on Pure and Applied Mathematics, 1984
- The Dirichlet problem for the equation of prescribed Gauss curvatureBulletin of the Australian Mathematical Society, 1983
- Sur les equations de Monge-Ampere. Imanuscripta mathematica, 1983
- Construction of a priori bounds for convex solutions of the Monge-Ampere equation by integral methodsUkrainian Mathematical Journal, 1978
- The dirichlet problem for the multidimensional monge-ampere equationRocky Mountain Journal of Mathematics, 1977