Calculus of Variations with Differential Forms
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arXiv
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| Format: | Preprint |
| Published: |
2017
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| _version_ | 1866916668060467200 |
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| author | Bandyopadhyay, Saugata Dacorogna, Bernard Sil, Swarnendu |
| author_facet | Bandyopadhyay, Saugata Dacorogna, Bernard Sil, Swarnendu |
| contents | We study integrals of the form $\int_Ωf\left( dω\right)$, where $1\leq k\leq n$, $f:Λ^{k}\rightarrow\mathbb{R}$ is continuous and $ω$ is a $\left(k-1\right)$-form. We introduce the appropriate notions of convexity, namely ext. one convexity, ext. quasiconvexity and ext. polyconvexity. We study their relations, give several examples and counterexamples. We finally conclude with an application to a minimization problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1712_00272 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Calculus of Variations with Differential Forms Bandyopadhyay, Saugata Dacorogna, Bernard Sil, Swarnendu Functional Analysis Analysis of PDEs Differential Geometry 49J10, 49J45 We study integrals of the form $\int_Ωf\left( dω\right)$, where $1\leq k\leq n$, $f:Λ^{k}\rightarrow\mathbb{R}$ is continuous and $ω$ is a $\left(k-1\right)$-form. We introduce the appropriate notions of convexity, namely ext. one convexity, ext. quasiconvexity and ext. polyconvexity. We study their relations, give several examples and counterexamples. We finally conclude with an application to a minimization problem. |
| title | Calculus of Variations with Differential Forms |
| topic | Functional Analysis Analysis of PDEs Differential Geometry 49J10, 49J45 |
| url | https://arxiv.org/abs/1712.00272 |