Ill-posedness of the Dirichlet problem for 2D Lagrangian mean curvature equation
Abstract
We investigate the Dirichlet problem of the two dimensional Lagrangian mean curvature equation in a bounded domain. Infinitely many C1, α (α∈ (0,15)) very weak solutions are built through Nash-Kuiper construction. Moreover, we note there are infinitely many C1, α very weak solutions that can not be improved to be C2, α.
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