Solvability of quasilinear elliptic equations with nonlinear boundary conditions. II (Q793221)

The author had previously [Trans. Am. Math. Soc. 273, 753-765 (1982; Zbl 0498.35039)] reduced the solvability of the second order quasilinear elliptic equation with nonlinear boundary condition \(Qu=0\) in \(\Omega\), \(Nu=0\) on \(\partial \Omega\), where \(\Omega\) is a smooth, bounded domain in \({\mathbb{R}}^ n\), to the establishment of certain apriori estimates on solutions of \(Qu=f\) in \(\Omega\), \(Nu=\phi\) on \(\partial \Omega\) as f and \(\phi\) range over appropriate collection of functions. The present work shows that \(\phi\) can be taken to be zero. Examples demonstrate the utility of this improved result.