Estimate of the gradient of a solution of the Dirichlet problem for Monge-Ampère type equations in a domain with nonsmooth boundary
This paper deals with the Dirichlet problem: \[ F_m(a;u)=f(x,u_x)\quad\text{in }\Omega,\quad u=0\quad\text{on }\partial\Omega,\tag{1} \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^n\), \(n\geq 2\), and \(F_m(a,u)\) is the operator of Monge-Ampère type investigated in \textit{N. M. Ivochkina}, the author and \textit{G. V. Yakunina} [J. Math. Sci., New York 73, No. 6, 663-673 (1995); translation from Probl. Mat. Anal. 13, 89-106 (1992; Zbl 0847.35043)]. The author obtains an estimate for the normal derivative of a viscous solution \(u\) to (1), near \(\partial\Omega\), when \(\partial\Omega\) is of class \(C^0\).
scientific article; zbMATH DE number 916348
scientific article