On the regularity of minimizers for scalar integral functionals with $(p,q)$-growth

@article{Bella2019OnTR,
  title={On the regularity of minimizers for scalar integral functionals with \$(p,q)\$-growth},
  author={P. Bella and M. Schaffner},
  journal={arXiv: Analysis of PDEs},
  year={2019}
}
  • P. Bella, M. Schaffner
  • Published 2019
  • Mathematics, Physics
  • arXiv: Analysis of PDEs
  • We revisit the question of regularity for minimizers of scalar autonomous integral functionals with so-called $(p,q)$-growth. In particular, we establish Lipschitz regularity under the condition $\frac{q}p<1+\frac{2}{n-1}$ for $n\geq3$ which improves a classical result due to Marcellini~[JDE'91]. 
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