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Abstract |
In this talk two kinds of boundary estimates for degenerate elliptic Monge -Ampere equations arising from study of isometric embeddings in Differential Geometry, will be introduced. As far as the classification of boundary degeneracy be concerned, one is non-characteristic degenerate and another is characteristic degenerate. The corresponding linearized operator is Tricomi type and Keldys type respectively. Their behaviors are quite different. By establishing a priori estimates for such two modeling boundary value problems we can derive the regularity of solutions to the relevant degenerate elliptic Monge-Ampere equations. Finally, some applications to geometric problems are presented. |
