American Institute of Mathematical Sciences

Advanced
May  2010, 27(2): 657-691. doi: 10.3934/dcds.2010.27.657

The Pullback equation for degenerate forms

Saugata Bandyopadhyay 1, , Bernard Dacorogna 2, and  Olivier Kneuss 2,

1. 

Department of Mathematical Sciences, IISER Kolkata, Mohanpur Campus, PO: BCKV Campus Main Office, Mohanpur - 741252, West Bengal, India
2. 

Section de Mathématiques, Station 8, EPFL, 1015 Lausanne, Switzerland, Switzerland

Received  October 2009 Revised  February 2010 Published  February 2010

We discuss the existence of a diffeomorphism $\varphi:\mathbb{R} ^{n}\rightarrow\mathbb{R}^{n}$ such that

φ ∗ (g) =f,

where $f,g:\mathbb{R}^{n}\rightarrow\Lambda^{k}$ are closed differential forms and $2\leq k\leq n-1.$

Keywords: Differential forms, Pullback equation., Darboux theorem.
Mathematics Subject Classification: Primary: 35Fxx; Secondary: 58A1.
Citation: Saugata Bandyopadhyay, Bernard Dacorogna, Olivier Kneuss. The Pullback equation for degenerate forms. Discrete and Continuous Dynamical Systems, 2010, 27 (2) : 657-691. doi: 10.3934/dcds.2010.27.657
[1]

Marcus A. Khuri. On the local solvability of Darboux's equation. Conference Publications, 2009, 2009 (Special) : 451-456. doi: 10.3934/proc.2009.2009.451
[2]

Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations and Control Theory, 2016, 5 (3) : 449-461. doi: 10.3934/eect.2016013
[3]

Anish Ghosh, Dubi Kelmer. A quantitative Oppenheim theorem for generic ternary quadratic forms. Journal of Modern Dynamics, 2018, 12: 1-8. doi: 10.3934/jmd.2018001
[4]

Eric L. Grinberg, Haizhong Li. The Gauss-Bonnet-Grotemeyer Theorem in space forms. Inverse Problems and Imaging, 2010, 4 (4) : 655-664. doi: 10.3934/ipi.2010.4.655
[5]

R.D.S. Oliveira, F. Tari. On pairs of differential $1$-forms in the plane. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 519-536. doi: 10.3934/dcds.2000.6.519
[6]

Henry Cohn, Nadia Heninger. Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding. Advances in Mathematics of Communications, 2015, 9 (3) : 311-339. doi: 10.3934/amc.2015.9.311
[7]

Carlos Gutierrez, Víctor Guíñez, Alvaro Castañeda. Quartic differential forms and transversal nets with singularities. Discrete and Continuous Dynamical Systems, 2010, 26 (1) : 225-249. doi: 10.3934/dcds.2010.26.225
[8]

Holger Heumann, Ralf Hiptmair, Cecilia Pagliantini. Stabilized Galerkin for transient advection of differential forms. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 185-214. doi: 10.3934/dcdss.2016.9.185
[9]

Olivier Hénot. On polynomial forms of nonlinear functional differential equations. Journal of Computational Dynamics, 2021, 8 (3) : 309-323. doi: 10.3934/jcd.2021013
[10]

Thierry Horsin, Peter I. Kogut, Olivier Wilk. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions. Mathematical Control and Related Fields, 2016, 6 (4) : 595-628. doi: 10.3934/mcrf.2016017
[11]

Sebastián Ferrer, Martin Lara. Families of canonical transformations by Hamilton-Jacobi-Poincaré equation. Application to rotational and orbital motion. Journal of Geometric Mechanics, 2010, 2 (3) : 223-241. doi: 10.3934/jgm.2010.2.223
[12]

Manuel de León, Juan Carlos Marrero, David Martín de Diego. Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics. Journal of Geometric Mechanics, 2010, 2 (2) : 159-198. doi: 10.3934/jgm.2010.2.159
[13]

Thierry Horsin, Peter I. Kogut. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. I. Existence result. Mathematical Control and Related Fields, 2015, 5 (1) : 73-96. doi: 10.3934/mcrf.2015.5.73
[14]

Sana Netchaoui, Mohamed Ali Hammami, Tomás Caraballo. Pullback exponential attractors for differential equations with delay. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1345-1358. doi: 10.3934/dcdss.2020367
[15]

Bernd Aulbach, Martin Rasmussen, Stefan Siegmund. Invariant manifolds as pullback attractors of nonautonomous differential equations. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 579-596. doi: 10.3934/dcds.2006.15.579
[16]

Mohamed Ali Hammami, Lassaad Mchiri, Sana Netchaoui, Stefanie Sonner. Pullback exponential attractors for differential equations with variable delays. Discrete and Continuous Dynamical Systems - B, 2020, 25 (1) : 301-319. doi: 10.3934/dcdsb.2019183
[17]

Weigu Li, Jaume Llibre, Hao Wu. Polynomial and linearized normal forms for almost periodic differential systems. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 345-360. doi: 10.3934/dcds.2016.36.345
[18]

Holger Heumann, Ralf Hiptmair. Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms. Discrete and Continuous Dynamical Systems, 2011, 29 (4) : 1471-1495. doi: 10.3934/dcds.2011.29.1471
[19]

Dorina Mitrea and Marius Mitrea. Boundary integral methods for harmonic differential forms in Lipschitz domains. Electronic Research Announcements, 1996, 2: 92-97.

[20]

Dorina Mitrea, Irina Mitrea, Marius Mitrea, Lixin Yan. Coercive energy estimates for differential forms in semi-convex domains. Communications on Pure and Applied Analysis, 2010, 9 (4) : 987-1010. doi: 10.3934/cpaa.2010.9.987

2021 Impact Factor: 1.588

Tools

Metrics

  • PDF downloads (68)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy