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Article Dans Une Revue Advances in Calculus of Variation Année : 2017

Calculus of Variations: A Differential Form Approach

Résumé

We study integrals of the form $\int_{\Omega}f\left( d\omega_1 , \ldots , d\omega_m \right), $ where $m \geq 1$ is a given integer, $1 \leq k_{i} \leq n$ are integers and $\omega_{i}$ is a $(k_{i}-1)$-form for all $1 \leq i \leq m$ and $ f:\prod_{i=1}^m \Lambda^{k_i}\left( \mathbb{R}^{n}\right) \rightarrow\mathbb{R}$ is a continuous function. We introduce the appropriate notions of convexity, namely vectorial ext. one convexity, vectorial ext. quasiconvexity and vectorial ext. polyconvexity. We prove weak lower semicontinuity theorems and weak continuity theorems and conclude with applications to minimization problems. These results generalize the corresponding results in both classical vectorial calculus of variations and the calculus of variations for a single differential form.
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Dates et versions

hal-01663264 , version 1 (13-12-2017)

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Citer

Swarnendu Sil. Calculus of Variations: A Differential Form Approach. Advances in Calculus of Variation, In press, ⟨10.1515/acv-2016-0058⟩. ⟨hal-01663264⟩

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