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Regularity for vectorial double phase functionals with two modulating coefficients and logarithmic-type growth

  • Yumi Kim
  • Jehan Oh
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Abstract

We study vector-valued local minimizers of double phase functionals with two modulating coefficients and logarithmic-type growth. The energy density is a(x)|Du|p+b(x)|Du|plog(e+|Du|), where the nonnegative coefficients a(·) and b(·) may vanish but their sum is bounded away from zero. Assuming that a(·) is uniformly continuous and that b(·) satisfies a vanishing log-Hölder continuity condition, we prove that minimizers are locally Hölder continuous for every exponent in (0,1). If both coefficients are Hölder continuous, then the gradient of a minimizer is locally Hölder continuous. The proof combines Gehring-type higher integrability with a comparison argument.

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Cite

BibTeXRIS
BibTeX
@misc{kim2026regularity,
  title = {{Regularity for vectorial double phase functionals with two modulating coefficients and logarithmic-type growth}},
  author = {Yumi Kim and Jehan Oh},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33479},
  eprint = {2609.33479},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33479},
}
RIS
TY  - UNPB
TI  - Regularity for vectorial double phase functionals with two modulating coefficients and logarithmic-type growth
AU  - Yumi Kim
AU  - Jehan Oh
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.33479
UR  - https://arxiv.org/abs/2609.33479
AB  - We study vector-valued local minimizers of double phase functionals with two modulating coefficients and logarithmic-type growth. The energy density is a(x)|Du|^p+b(x)|Du|^plog(e+|Du|), where the nonnegative coefficients a(·) and b(·) may vanish but their sum is bounded away from zero. Assuming that a(·) is uniformly continuous and that b(·) satisfies a vanishing log-Hölder continuity condition, we prove that minimizers are locally Hölder continuous for every exponent in (0,1). If both coefficients are Hölder continuous, then the gradient of a minimizer is locally Hölder continuous. The proof combines Gehring-type higher integrability with a comparison argument.
ER  -