Singular orthotropic functionals with nonstandard growth conditions

• Pierre Bousquet ^[1] ; Lorenzo Brasco ^[2] ; Chiara Leone ^[3]
  1. [1] Université de Toulouse

     Université de Toulouse

     Arrondissement de Toulouse, Francia

     
  2. [2] University of Ferrara

     University of Ferrara

     Ferrara, Italia

     
  3. [3] University of Naples Federico II

     University of Naples Federico II

     Nápoles, Italia

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 2, 2024, págs. 753-802
• Idioma: inglés
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• Resumen

  • We pursue the study of a model convex functional with orthotropic structure and nonstandard growth conditions, this time focusing on the sub-quadratic case. We prove that bounded local minimizers are locally Lipschitz. No restrictions on the ratio between the highest and the lowest growth rates are needed. The result holds also in presence of a non-autonomous lower order term, under sharp integrability assumptions. Finally, we prove higher differentiability of bounded local minimizers as well.