| 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 $\mathcal{C}^{1,\alpha}$ 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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