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arXiv · 2409.04816

Ill-posedness of the Dirichlet problem for 2D Lagrangian mean curvature equation

Wentao Cao·Zhehui Wang
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Abstract

We investigate the Dirichlet problem of the two dimensional Lagrangian mean curvature equation in a bounded domain. Infinitely many $C^{1, \alpha} (\alpha\in (0,\frac{1}{5}))$ very weak solutions are built through Nash-Kuiper construction. Moreover, we note there are infinitely many $C^{1, \alpha}$ very weak solutions that can not be improved to be $C^{2, \alpha}$.

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Wentao Cao, Zhehui Wang. 2024-09-07. Ill-posedness of the Dirichlet problem for 2D Lagrangian mean curvature equation. https://arxiv.org/abs/2409.04816

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