English

Regularity for multi-phase variational problems

Analysis of PDEs 2018-07-10 v1

Abstract

We prove C1,νC^{1,\nu} regularity for local minimizers of the \oh{multi-phase} energy: \begin{flalign*} w \mapsto \int_{\Omega}\snr{Dw}^{p}+a(x)\snr{Dw}^{q}+b(x)\snr{Dw}^{s} \ dx, \end{flalign*} under sharp assumptions relating the couples (p,q)(p,q) and (p,s)(p,s) to the H\"older exponents of the modulating coefficients a()a(\cdot) and b()b(\cdot), respectively.

Keywords

Cite

@article{arxiv.1807.02880,
  title  = {Regularity for multi-phase variational problems},
  author = {Cristiana De Filippis and Jehan Oh},
  journal= {arXiv preprint arXiv:1807.02880},
  year   = {2018}
}
R2 v1 2026-06-23T02:54:12.264Z