Direct methods in the calculus of variations for differential forms
نویسندگان
چکیده
*Correspondence: [email protected] Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, P.R. China Abstract 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
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