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Main Authors: Hakobyan, Aram, Poghosyan, Michael, Shahgholian, Henrik
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2602.14305
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author Hakobyan, Aram
Poghosyan, Michael
Shahgholian, Henrik
author_facet Hakobyan, Aram
Poghosyan, Michael
Shahgholian, Henrik
contents We prove that the gradient of any bounded subharmonic function is upper semi-continuous, provided that its super-level sets can be touched from the exterior by uniform $C^{1,\text{Dini}}$ domains at every point. This idea extends to a class of general operators, as well as to the boundary behaviour of the gradient of solutions of the Dirichlet problem in a domain whose boundary satisfy this geometric condition.
format Preprint
id arxiv_https___arxiv_org_abs_2602_14305
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Partial regularity of the gradient for subsolutions
Hakobyan, Aram
Poghosyan, Michael
Shahgholian, Henrik
Analysis of PDEs
35B65
We prove that the gradient of any bounded subharmonic function is upper semi-continuous, provided that its super-level sets can be touched from the exterior by uniform $C^{1,\text{Dini}}$ domains at every point. This idea extends to a class of general operators, as well as to the boundary behaviour of the gradient of solutions of the Dirichlet problem in a domain whose boundary satisfy this geometric condition.
title Partial regularity of the gradient for subsolutions
topic Analysis of PDEs
35B65
url https://arxiv.org/abs/2602.14305