The Neumann function and the L p Neumann problem in chord-arc domains
Year: 2025
Type: article
Abstract: We construct the Neumann function in a 1-sided chord-arc domain (i.e., a uniform domain with an Ahlfors regular boundary), and establish size and Hölder continuity estimates up to the boundary. We then obtain a Kenig-Pipher type theorem, in which L p solvability of the Neumann problem is shown to yield solvability in L q for 1 < q < p , and in the Hardy space H 1 , in 2-sided chord-arc domains, under suitable background hypotheses.
Source: Advanced Nonlinear Studies
Authors: Steve Hofmann, Derek Sparrius
Institutions: University of Missouri, Truman State University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,469
OpenAlex ID: W4407890879