【摘要】 <正> 二阶椭圆型方程的极值原理,不仅推广了古典极值原理,而且在解的Holder模估计上也起到了作用(见[22],[32]-[34].不过这类极值原理的陈述和证明,却至少散布在[4]-[9],[11]-[14]这一系列文献中,而且有的文献很难查找,学起更多还原

【Abstract】 The Aleksandrov-Bakel’man maximum principles are systematically treated in this paper following the idea that the L∞-estimate of a solution can be obtained by estimating the height of the graph of the convex envelope of the solution. To realize this idea, the facts about convex hypersurfaces and convex functions presented in § 1 are required.Bymeans of the normal curvature derived from the normal mapping, a geometric lemma for estimating the height of a convex hyper surface is established in §2.Owing to this lemma, only the calculation and the estimation of the normal curvature are neede, which are given in §3, from which the maximum principles are deduced in §4.Theorem 4.1 in the paper is the correction of Theorem 17.4 in[22] in a sense, and other connections with known results are indicated in the Notes at the end of the paper.更多还原