PreprintarXiv licencearXiv
Global Hölder solvability for parabolic equations with interior Morrey data
Abstract
We prove global Hölder solvability for uniformly parabolic divergence-form equations with locally finite measure data under an interior Morrey growth condition and a capacity density condition on the spatial domain. The parabolic distance to the initial and lateral boundary is assumed bounded on the source support. For nonnegative data, we establish necessity results that demonstrate the sharpness of the growth and domain assumptions. We also derive estimates for divergence forcing, prove solvability for equations with lower-order terms, and obtain convergence rates in periodic homogenization.
Related
- Interior regularity of mixed local-nonlocal parabolic semilinear equations
- Asymptotically Hölder gradient regularity for degenerate or singular parabolic normalized $ p$-Laplace equations
- Hölder regularity of solutions to parabolic equations associated with fractional p-Laplacian type operators
- Global Hölder estimates for linearized Monge-Ampère equations in divergence form with applications to dual semigeostrophic equations and periodic homogenization
- Global solvability of the heat equations in two unbounded domains and the interface
BibTeX
@misc{hara2026global,
title = {{Global Hölder solvability for parabolic equations with interior Morrey data}},
author = {Takanobu Hara},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37528},
eprint = {2610.37528},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37528},
}
RIS
TY - UNPB
TI - Global Hölder solvability for parabolic equations with interior Morrey data
AU - Takanobu Hara
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37528
UR - https://arxiv.org/abs/2610.37528
AB - We prove global Hölder solvability for uniformly parabolic divergence-form equations with locally finite measure data under an interior Morrey growth condition and a capacity density condition on the spatial domain. The parabolic distance to the initial and lateral boundary is assumed bounded on the source support. For nonnegative data, we establish necessity results that demonstrate the sharpness of the growth and domain assumptions. We also derive estimates for divergence forcing, prove solvability for equations with lower-order terms, and obtain convergence rates in periodic homogenization.
ER -