The Poisson problem with mixed boundary conditions in Sobolev and Besov spaces in non-smooth domains
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- by Irina Mitrea and Marius Mitrea PDF
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Abstract:
We introduce certain Sobolev-Besov spaces which are particularly well adapted for measuring the smoothness of data and solutions of mixed boundary value problems in Lipschitz domains. In particular, these are used to obtain sharp well-posedness results for the Poisson problem for the Laplacian with mixed boundary conditions on bounded Lipschitz domains which satisfy a suitable geometric condition introduced by R. Brown in (1994). In this context, we obtain results which generalize those by D. Jerison and C. Kenig (1995) as well as E. Fabes, O. Mendez and M. Mitrea (1998). Applications to Hodge theory and the regularity of Green operators are also presented.References
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Additional Information
- Irina Mitrea
- Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
- MR Author ID: 634131
- Email: im3p@virginia.edu
- Marius Mitrea
- Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211
- MR Author ID: 341602
- ORCID: 0000-0002-5195-5953
- Email: marius@math.missouri.edu
- Received by editor(s): May 3, 2005
- Published electronically: April 11, 2007
- Additional Notes: The first author was supported in part by NSF grant DMS - 0547944 and a FEST grant from the University of Virginia
The second author was supported in part by the NSF grants DMS - 0400639 and DMS FRG - 0456306. - © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 4143-4182
- MSC (2000): Primary 45E05, 47A05; Secondary 35J25, 42B20
- DOI: https://doi.org/10.1090/S0002-9947-07-04146-3
- MathSciNet review: 2309180