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Full flexibility of the Monge-Ampère system in codimension
Wentao Cao, Jonas Hirsch, Dominik Inauen +1
We prove that solutions to the Monge-Ampère system in dimension and codimension , where denotes the Janet dimension, are dense in the spac…
Isometric Immersions and Weak Solutions to the Darboux Equation
Wentao Cao, Jonas Hirsch, Dominik Inauen
We study the Darboux equation, a fundamental PDE arising in the theory of isometric immersions of two-dimensional Riemannian manifolds into , in the low-regularity re…
A Nash-Kuiper theorem for isometric immersions beyond Borisov's exponent
Wentao Cao, Jonas Hirsch, Dominik Inauen
Given any short immersion from an -dimensional bounded and simply connected domain into and any Hölder exponent , we construct a …
Ill-posedness of the Dirichlet problem for 2D Lagrangian mean curvature equation
Wentao Cao, Zhehui Wang
We investigate the Dirichlet problem of the two dimensional Lagrangian mean curvature equation in a bounded domain. Infinitely many very weak solu…
very weak solutions to the two dimensional Monge-Ampére equation
Wentao Cao, Jonas Hirsch, Dominik Inauen
For any , we show that very weak solutions to the two-dimensional Monge-Ampère equation with regularity are dense in the space of continuous functions. Thi…