Year: 2026
Type: article
Abstract: For any subharmonic function u , we prove that $$|\partial _j u|$$ | ∂ j u | ( $$j=1, \ldots , n$$ j = 1 , … , n ) is upper semi-continuous, provided that the super-level sets of u can be touched from the exterior by uniform $$C^{1,\text {Dini}}$$ C 1 , 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 satisfies this geometric condition.
Authors: A. Hakobyan, M. Poghosyan, H. Shahgholian
Institutions: Yerevan State University, KTH Royal Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7166308781