The Neumann function and the L p Neumann problem in chord-arc domains
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 yi...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-02-01
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| Series: | Advanced Nonlinear Studies |
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| Online Access: | https://doi.org/10.1515/ans-2023-0171 |
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| author | Hofmann Steve Sparrius Derek |
| author_facet | Hofmann Steve Sparrius Derek |
| author_sort | Hofmann Steve |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5d754b2c8fc74ed3b1c2271e86f7204d |
| institution | DOAJ |
| issn | 2169-0375 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj-art-5d754b2c8fc74ed3b1c2271e86f7204d2025-08-20T03:12:34ZengDe GruyterAdvanced Nonlinear Studies2169-03752025-02-0125231334910.1515/ans-2023-0171The Neumann function and the L p Neumann problem in chord-arc domainsHofmann Steve0Sparrius Derek1Department of Mathematics, University of Missouri, Columbia, MO65211, USADepartment of Mathematics, Truman State University, Kirksville, MO63501, USAWe 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.https://doi.org/10.1515/ans-2023-0171neumann functionneumann problemsecond order elliptic equationschord-arc domains35j2542b3742b30 |
| spellingShingle | Hofmann Steve Sparrius Derek The Neumann function and the L p Neumann problem in chord-arc domains Advanced Nonlinear Studies neumann function neumann problem second order elliptic equations chord-arc domains 35j25 42b37 42b30 |
| title | The Neumann function and the L
p Neumann problem in chord-arc domains |
| title_full | The Neumann function and the L
p Neumann problem in chord-arc domains |
| title_fullStr | The Neumann function and the L
p Neumann problem in chord-arc domains |
| title_full_unstemmed | The Neumann function and the L
p Neumann problem in chord-arc domains |
| title_short | The Neumann function and the L
p Neumann problem in chord-arc domains |
| title_sort | neumann function and the l p neumann problem in chord arc domains |
| topic | neumann function neumann problem second order elliptic equations chord-arc domains 35j25 42b37 42b30 |
| url | https://doi.org/10.1515/ans-2023-0171 |
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