Solutions of H-systems using the Green function. Bulletin

P. AMSTER, M. C. MARIANI Y D. RIAL

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN

Año: 2000 vol. 7 p. 487 - 492

1370-1444

We consider the Dirichlet problem for the prescribed mean curvature system $\Delta X = 2H(u,v,X)X_\times X_v$ in $\Omega$ and $X = g$ on $\partial\Omega$ for a vector function $X:\Omega\rightarrow R^3$, where $\Omega$ is a smooth bounded domain in $R^2$. This problem and the general Plateau problem with $H=$constant and $H=H(X)$ have been studied by several authors using variational methods. We use topological methods to study the problem in the case $H=H(u,v)$