New Examples on Lavrentiev Gap Using Fractals

Khripunova Balci A, Diening L, Surnachev M (2020)
Calculus of Variations and Partial Differential Equations 59(5): 180.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Zhikov showed 1986 with his famous checkerboard example that functionals with variable exponents can have a Lavrentiev gap. For this example it was crucial that the exponent had a saddle point whose value was exactly the dimension. In 1997 he extended this example to the setting of the double phase potential. Again it was important that the exponents crosses the dimensional threshold. Therefore, it was conjectured that the dimensional threshold plays an important role for the Lavrentiev gap. We show that this is not the case. Using fractals we present new examples for the Lavrentiev gap and non-density of smooth functions. We apply our method to the setting of variable exponents, the double phase potential and weightedp-energy.
Stichworte
Applied Mathematics; Analysis
Erscheinungsjahr
2020
Zeitschriftentitel
Calculus of Variations and Partial Differential Equations
Band
59
Ausgabe
5
Art.-Nr.
180
ISSN
0944-2669
eISSN
1432-0835
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
Page URI
https://pub.uni-bielefeld.de/record/2948279

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Khripunova Balci A, Diening L, Surnachev M. New Examples on Lavrentiev Gap Using Fractals. Calculus of Variations and Partial Differential Equations. 2020;59(5): 180.
Khripunova Balci, A., Diening, L., & Surnachev, M. (2020). New Examples on Lavrentiev Gap Using Fractals. Calculus of Variations and Partial Differential Equations, 59(5), 180. doi:10.1007/s00526-020-01818-1
Khripunova Balci, A., Diening, L., and Surnachev, M. (2020). New Examples on Lavrentiev Gap Using Fractals. Calculus of Variations and Partial Differential Equations 59:180.
Khripunova Balci, A., Diening, L., & Surnachev, M., 2020. New Examples on Lavrentiev Gap Using Fractals. Calculus of Variations and Partial Differential Equations, 59(5): 180.
A. Khripunova Balci, L. Diening, and M. Surnachev, “New Examples on Lavrentiev Gap Using Fractals”, Calculus of Variations and Partial Differential Equations, vol. 59, 2020, : 180.
Khripunova Balci, A., Diening, L., Surnachev, M.: New Examples on Lavrentiev Gap Using Fractals. Calculus of Variations and Partial Differential Equations. 59, : 180 (2020).
Khripunova Balci, Anna, Diening, Lars, and Surnachev, Mikhail. “New Examples on Lavrentiev Gap Using Fractals”. Calculus of Variations and Partial Differential Equations 59.5 (2020): 180.
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2020-12-03T12:54:40Z
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arXiv: arXiv:1906.04639

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