Singular orthotropic functionals with nonstandard growth conditions

  • Pierre Bousquet

    Université de Toulouse, CNRS, France
  • Lorenzo Brasco

    Università degli Studi di Ferrara, Italy
  • Chiara Leone

    Università degli Studi di Napoli Federico II, Italy
Singular orthotropic functionals with nonstandard growth conditions cover
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Abstract

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.

Cite this article

Pierre Bousquet, Lorenzo Brasco, Chiara Leone, Singular orthotropic functionals with nonstandard growth conditions. Rev. Mat. Iberoam. (2023), published online first

DOI 10.4171/RMI/1446