Ammann, Bernd and Grosse, Nadine and Nistor, Victor (2019) Analysis and boundary value problems on singular domains: An approach via bounded geometry. COMPTES RENDUS MATHEMATIQUE, 357 (6). pp. 487-493. ISSN 1631-073X, 1778-3569
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We prove well-posedness and regularity results for elliptic boundary value problems on certain singular domains that are conformally equivalent to manifolds with boundary and bounded geometry. Our assumptions are satisfied by the domains with a smooth set of singular cuspidal points, and hence our results apply to the class of domains with isolated oscillating conical singularities. In particular, our results generalize the classical L-2-wellposedness result of Kondratiev for the Laplacian on domains with conical points. However, our domains and coefficients are too general to allow for singular function expansions of the solutions similar to the ones in Kondratiev's theory. The proofs are based on conformal changes of metric, on the differential geometry of manifolds with boundary and bounded geometry, and on our earlier geometric and analytic results on such manifolds. (C) 2019 Academie des sciences. Published by Elsevier Masson SAS.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | NEUMANN PROBLEM; MANIFOLDS; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Bernd Ammann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Apr 2020 05:31 |
| Last Modified: | 14 Apr 2020 05:31 |
| URI: | https://pred.uni-regensburg.de/id/eprint/26873 |
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