Lancaster, Kirk E. Nonexistence of some nonparametric surfaces of prescribed mean curvature. (English) Zbl 0602.35040 Proc. Am. Math. Soc. 96, 187-188 (1986). 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. Cited in 2 Documents 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) Keywords:nonexistence; nonparametric surfaces; Dirichlet problem; prescribed mean curvature; zero boundary value PDFBibTeX XMLCite \textit{K. E. Lancaster}, Proc. Am. Math. Soc. 96, 187--188 (1986; Zbl 0602.35040) Full Text: DOI