Direct methods in the calculus of variations for differential forms

Journal of inequalities and applications

Tingting Wang¹ 

关键词: weak lower semicontinuity;    differential forms;    variational problem;    direct methods;    existence theorem;   

DOI  :  10.1186/1029-242X-2013-407

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The purpose of this paper is to establish the general theory of the direct methods to functionals I defined on the Grassmann algebra employing the classical approaches. In this paper, various notions of convexity conditions for weak lower semicontinuity of I are discussed, and existence theorems for minimizers of I are obtained. Lastly, we present some examples to illustrate our main results. MSC:35A15, 58A10.

【 授权许可】

CC BY