Hölder regularity for logarithmic double phase problems
Abstract
We investigate boundedness and regularity properties of weak solutions to a class of generalized logarithmic double phase equations with variable exponents. The considered operators arise from Musielak-Orlicz type energies of logarithmic double phase type and exhibit nonstandard growth features. Under general structural assumptions, we derive a priori boundedness estimates in the subcritical setting and establish boundedness of weak solutions also in the presence of critical growth terms. In addition, we prove global Hölder continuity up to the boundary by means of the De Giorgi iteration scheme, localization arguments, and the frozen functional technique. The obtained results extend several existing regularity results for double phase and related nonstandard growth problems.
Related
- The Hölder interpolative gap bound for degenerate parabolic double phase problems
- Regularity for vectorial double phase functionals with two modulating coefficients and logarithmic-type growth
- Borderline double phase functionals with powers of the logarithm: regularity in the vectorial case
- Partial regularity for local minimizers of functionals with double-phase Orlicz growth
- Double-Phase Neumann Problems with Variable Growth on Metric Measure Spaces
BibTeX
@misc{ho2026hölder,
title = {{Hölder regularity for logarithmic double phase problems}},
author = {Ky Ho and Yun-Ho Kim and Patrick Winkert},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2607.16749},
eprint = {2607.16749},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.16749},
}
RIS
TY - UNPB
TI - Hölder regularity for logarithmic double phase problems
AU - Ky Ho
AU - Yun-Ho Kim
AU - Patrick Winkert
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2607.16749
UR - https://arxiv.org/abs/2607.16749
AB - We investigate boundedness and regularity properties of weak solutions to a class of generalized logarithmic double phase equations with variable exponents. The considered operators arise from Musielak-Orlicz type energies of logarithmic double phase type and exhibit nonstandard growth features. Under general structural assumptions, we derive a priori boundedness estimates in the subcritical setting and establish boundedness of weak solutions also in the presence of critical growth terms. In addition, we prove global Hölder continuity up to the boundary by means of the De Giorgi iteration scheme, localization arguments, and the frozen functional technique. The obtained results extend several existing regularity results for double phase and related nonstandard growth problems.
ER -