| Abstract: |
| We study flexibility of weak solutions to the Monge-Ampere system (MA) via convex integration.
This new system of Pdes is an extension of the Monge-Ampere equation in d=2 dimensions, naturally arising from the prescribed curvature problem and closely related to the classical problem of isometric immersions.
Our main results achieve density in the set of subsolutions, of the Holder C1,α solutions to the Von Karman system which is the weak formulation of (MA). We will present a panorama of recent results in this context, exhibiting regularity dependence on the dimension and codimension of the problem. |
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