The common root of the geometric conditions in Serrin's lower semicontinuity theorem

被引：3
作者：
Gori, Michele
Maggi, Francesco
机构：
[1] Univ Pisa, Dipartimento Matemat L Tonelli, I-56127 Pisa, Italy
[2] Univ Florence, Dipartimento Matemat U Dini, I-50134 Florence, Italy
来源：
ANNALI DI MATEMATICA PURA ED APPLICATA | 2005年 / 184卷 / 01期
关键词：
lower semicontinuity; convexity; strict convexity; calculus of variations; demicoercivity;
D O I：
10.1007/s10231-003-0091-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we extend a classical lower semicontinuity theorem by J. Serrin. We achieve this result by applying an approximation method for convex functions where, instead of supporting hyperplanes, certain maximal cones are considered. This also allows us to give the characterization of the class of functions that can be written as a countable supremum of strictly convex ones.
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页码：95 / 114
页数：20
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