Notions of affinity in calculus of variations with differential forms
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Abstract
Ext-int. one affine functions are functions affine in the direction of one-divisible exterior forms with respect to the exterior product in one variable and with respect to the interior product in the other. The purpose of this article is to prove a characterization theorem for this class of functions, which plays an important role in the calculus of variations for differential forms.
Funding statement: The research of S. Bandyopadhyay was partially supported by a SERB research project titled “Pullback Equation for Differential Forms”.
We have benefited of interesting discussions with Professor Bernard Dacorogna. Part of this work was completed during visits of S. Bandyopadhyay to EPFL, whose hospitality and support is gratefully acknowledged.
References
[1] Bandyopadhyay S., Dacorogna B. and Sil S., Calculus of variations with differential forms, J. Eur. Math. Soc. (JEMS) 17 (2015), no. 4, 1009–1039. 10.4171/JEMS/525Suche in Google Scholar
[2] Bandyopadhyay S. and Sil S., Exterior convexity and classical calculus of variations, ESAIM Control Optim. Calc. Var., to appear. 10.1051/cocv/2015007Suche in Google Scholar
[3] Barroso A. C. and Matias J., Necessary and sufficient conditions for existence of solutions of a variational problem involving the curl, Discrete Contin. Dyn. Syst. 12 (2005), 97–114. 10.3934/dcds.2005.12.97Suche in Google Scholar
[4] Csató G., Dacorogna B. and Kneuss O., The Pullback Equation for Differential Forms, Progr. Nonlinear Differential Equations Appl. 83, Birkhäuser, Basel, 2012. 10.1007/978-0-8176-8313-9Suche in Google Scholar
[5] Dacorogna B., Direct Methods in the Calculus of Variations, 2nd ed., Appl. Math. Sci. 78, Springer, New York, 2007. Suche in Google Scholar
[6] Dacorogna B. and Fonseca I., A-B quasiconvexity and implicit partial differential equations, Calc. Var. Partial Differential Equations 14 (2002), 115–149. 10.1007/s005260100092Suche in Google Scholar
[7] Dacorogna B. and Kneuss O., Divisibility in Grassmann algebra, Linear Multilinear Algebra 59 (2011), no. 11, 1201–1220. 10.1080/03081087.2010.495389Suche in Google Scholar
[8] Sil S., Ph.D. thesis, EPFL, in preparation. Suche in Google Scholar
© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- The one-dimensional model for d-cones revisited
- Noether’s theorem and the Willmore functional
- An anisotropic bimodal energy for the segmentation of thin tubes and its approximation with Γ-convergence
- Regularity results for solutions to the c-Plateau problem with free boundary having small singular set, and generally in codimension zero
- On linear degenerate elliptic PDE systems with constant coefficients
- Notions of affinity in calculus of variations with differential forms
Artikel in diesem Heft
- Frontmatter
- The one-dimensional model for d-cones revisited
- Noether’s theorem and the Willmore functional
- An anisotropic bimodal energy for the segmentation of thin tubes and its approximation with Γ-convergence
- Regularity results for solutions to the c-Plateau problem with free boundary having small singular set, and generally in codimension zero
- On linear degenerate elliptic PDE systems with constant coefficients
- Notions of affinity in calculus of variations with differential forms
