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arxiv: 1809.06302 · v1 · pith:UHTEX4DLnew · submitted 2018-09-17 · 🧮 math.DG

The Dirichlet problem for the α-singular minimal surface equation

classification 🧮 math.DG
keywords alphadirichletequationminimalomegaproblemsingularsurface
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Let $\Omega\subset\r^n$ be a bounded mean convex domain. If $\alpha<0$, we prove the existence and uniqueness of classical solutions of the Dirichlet problem in $\Omega$ for the $\alpha$-singular minimal surface equation with arbitrary continuous boundary data.

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