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Nonexistence of some nonparametric surfaces of prescribed mean curvature. (English) Zbl 0602.35040

If \(\Omega \subset {\mathbb{R}}^ 2\) has a reentrant corner, the Dirichlet problem for the equation of prescribed mean curvature H with zero boundary value has no solution when H has constant nonzero sign.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
35J25 Boundary value problems for second-order elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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