On the Dirichlet problem for Lagrangian phase equation with critical and supercritical phase

Siyuan Lu

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On the Dirichlet problem for Lagrangian phase equation with critical and supercritical phase

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arxiv 2204.05420 v2 pith:BYPAS2CH submitted 2022-04-11 math.AP math.DG

On the Dirichlet problem for Lagrangian phase equation with critical and supercritical phase

Siyuan Lu This is my paper

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keywords phasecriticaldirichletequationlagrangianproblemsupercriticalcase

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In this paper, we solve the Dirichlet problem for Lagrangian phase equation with critical and supercritical phase. A crucial ingredient is the interior $C^2$ estimate. Our result is sharp in the sense that there exist singular solutions in the subcritical phase case.

On the Dirichlet problem for Lagrangian phase equation with critical and supercritical phase

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