A family of nonlinear resolvents
Let \(U\subset \mathbb{R}^k\) be a nonvoid, open, bounded and strictly convex set. With each continuous function on \(\partial U\), the author associates a nonlinear resolvent, corresponding to the non-homogeneous Dirichlet problem for the Monge-Ampère equation. The resolvent consists of increasing operators on \(L^{\infty }(U)\). This sharpens and extends previous results of the author [Rev. Roum. Math. Pures Appl. 40, No. 7-8, 691--710 (1995; Zbl 0869.31014) and ibid. 46, No. 1, 125--136 (2001; Zbl 1046.35036)]. The treatement is carried out in the spirit of \textit{C. Dellacherie} [Potential theory, Proc. Int. Conf., Nagoya/Jap. 1990, 25--32 (1992; Zbl 0762.31005)].
scientific article; zbMATH DE number 5008871