The Lavrentiev phenomenon in calculus of variations with differential forms
Khripunova Balci A, Surnachev M (2024)
Calculus of Variations and Partial Differential Equations 63(3): 62.
Zeitschriftenaufsatz
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Khripunova Balci, AnnaUniBi 
;
Surnachev, Mikhail
;
Surnachev, MikhailEinrichtung
Abstract / Bemerkung
**Abstract**
In this article we study convex non-autonomous variational problems with differential forms and corresponding function spaces. We introduce a general framework for constructing counterexamples to the Lavrentiev gap, which we apply to several models, including the double phase, borderline case of double phase potential, and variable exponent. The results for the borderline case of double phase potential provide new insights even for the scalar case, i.e., variational problems with 0-forms.
In this article we study convex non-autonomous variational problems with differential forms and corresponding function spaces. We introduce a general framework for constructing counterexamples to the Lavrentiev gap, which we apply to several models, including the double phase, borderline case of double phase potential, and variable exponent. The results for the borderline case of double phase potential provide new insights even for the scalar case, i.e., variational problems with 0-forms.
Erscheinungsjahr
2024
Zeitschriftentitel
Calculus of Variations and Partial Differential Equations
Band
63
Ausgabe
3
Art.-Nr.
62
Urheberrecht / Lizenzen
ISSN
0944-2669
eISSN
1432-0835
Page URI
https://pub.uni-bielefeld.de/record/2987293
Zitieren
Khripunova Balci A, Surnachev M. The Lavrentiev phenomenon in calculus of variations with differential forms. Calculus of Variations and Partial Differential Equations. 2024;63(3): 62.
Khripunova Balci, A., & Surnachev, M. (2024). The Lavrentiev phenomenon in calculus of variations with differential forms. Calculus of Variations and Partial Differential Equations, 63(3), 62. https://doi.org/10.1007/s00526-024-02664-1
Khripunova Balci, Anna, and Surnachev, Mikhail. 2024. “The Lavrentiev phenomenon in calculus of variations with differential forms”. Calculus of Variations and Partial Differential Equations 63 (3): 62.
Khripunova Balci, A., and Surnachev, M. (2024). The Lavrentiev phenomenon in calculus of variations with differential forms. Calculus of Variations and Partial Differential Equations 63:62.
Khripunova Balci, A., & Surnachev, M., 2024. The Lavrentiev phenomenon in calculus of variations with differential forms. Calculus of Variations and Partial Differential Equations, 63(3): 62.
A. Khripunova Balci and M. Surnachev, “The Lavrentiev phenomenon in calculus of variations with differential forms”, Calculus of Variations and Partial Differential Equations, vol. 63, 2024, : 62.
Khripunova Balci, A., Surnachev, M.: The Lavrentiev phenomenon in calculus of variations with differential forms. Calculus of Variations and Partial Differential Equations. 63, : 62 (2024).
Khripunova Balci, Anna, and Surnachev, Mikhail. “The Lavrentiev phenomenon in calculus of variations with differential forms”. Calculus of Variations and Partial Differential Equations 63.3 (2024): 62.
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Preprint: 10.48550/arXiv.2305.04726
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