Regularity for vectorial double phase functionals with two modulating coefficients and logarithmic-type growth
Year: 2026
Type: preprint
Abstract: We study vector-valued local minimizers of double phase functionals with two modulating coefficients and logarithmic-type growth. The energy density is $a(x)|Du|^p+b(x)|Du|^p\log(e+|Du|)$, where the nonnegative coefficients $a(\cdot)$ and $b(\cdot)$ may vanish but their sum is bounded away from zero. Assuming that $a(\cdot)$ is uniformly continuous and that $b(\cdot)$ 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.
Source: arXiv (Cornell University)
Authors: Kim, Yumi, Oh, Jehan
Institution: Kyungpook National University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1351423076, G1536775404
OpenAlex ID: W7214796448