Infinite boundary value problems for surfaces of prescribed mean curvature (Q1088149)

The Dirichlet problem for surfaces of prescribed mean curvature consists in determining a function \(u\in C^ 2(\Omega)\) satisfying the equation \[ (1+| Du|^ 2)\Delta u-\sum^{n}_{i,j=1}D_ iuD_ juD_{ij}u-nH(x)(1+| Du|^ 2)^{3/2}=0 \] in a bounded domain \(\Omega\) and some conditions on \(\partial \Omega\). The author proves an existence and uniqueness theorem for the case \(\lim_{y\to x} u(y)=+\infty\), \(x\in \Gamma_ 1\), \(\lim_{y\to x} u(y)=-\infty\), \(x\in \Gamma_ 2\), where \(\Gamma_ 1\), \(\Gamma_ 2\) are open (not empty), disjoint subsets of \(\partial \Omega\).