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On a necessary condition in the calculus of variations in Sobolev spaces with variable exponent

Volume 41 / 2014

Elhoussine Azroul, Meryem El Lekhlifi, Badr Lahmi, Abdelfattah Touzani Applicationes Mathematicae 41 (2014), 165-174 MSC: 46E35, 49K21, 91G80. DOI: 10.4064/am41-2-4

Abstract

We prove an approximation theorem in generalized Sobolev spaces with variable exponent $W^{1,p(\cdot )}(\varOmega )$ and we give an application of this approximation result to a necessary condition in the calculus of variations.

Authors

  • Elhoussine AzroulLAMA, Faculté des Sciences Dhar El Mahraz
    Université Sidi Mohamed Ben Abdellah
    BP 1796 Atlas
    Fès, Morocco
    e-mail
  • Meryem El LekhlifiLaboratoire d'Analyse Mathématique et Applications (LAMA)
    Faculté des Sciences Dhar El Mahraz
    Université Sidi Mohamed Ben Abdellah
    BP 1796 Atlas
    Fès, Moroccco
    e-mail
  • Badr LahmiLaboratoire d'Analyse Mathématique et Applications (LAMA)
    Faculté des Sciences Dhar El Mahraz
    Université Sidi Mohamed Ben Abdellah
    BP 1796 Atlas
    Fès, Morocco
    e-mail
  • Abdelfattah TouzaniLaboratoire d'Analyse Mathématique et Applications (LAMA)
    Faculté des Sciences Dhar El Mahraz
    Université Sidi Mohamed Ben Abdellah
    BP 1796 Atlas
    Fès, Morocco
    e-mail

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