The A. D. Aleksandrov maximum principle
The very interesting paper under review is devoted to the maximum principle of A. D. Aleksandrov which is one of the most beautiful applications of geometric ideas in the theory of the partial differential equations. After a short historical survey with rich reference links about the original result of Aleksandrov and its various outgrowths and applications, the author proposes some results related to the analysis of convex and convex-monotone holes. In particular, estimates for the maximum of solution to a Dirichlet problem for nondivergence form elliptic equations are derived. Moreover, local estimates are given for solutions to the degenerate Venttsel problem as well as to one- and two-phase Venttsel problems. A collection of the corresponding results for parabolic equations is also proposed. Highly recommended paper!
nondivergence form elliptic and parabolic equations
scientific article; zbMATH DE number 5319770
scientific article