Spectral estimates for resolvent differences of self-adjoint elliptic operators
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2010
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| _version_ | 1866916285880729600 |
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| author | Behrndt, Jussi Langer, Matthias Lotoreichik, Vladimir |
| author_facet | Behrndt, Jussi Langer, Matthias Lotoreichik, Vladimir |
| contents | The notion of quasi boundary triples and their Weyl functions is an abstract concept to treat spectral and boundary value problems for elliptic partial differential equations. In the present paper the abstract notion is further developed, and general theorems on resolvent differences belonging to operator ideals are proved. The results are applied to second order elliptic differential operators on bounded and exterior domains, and to partial differential operators with $δ$ and $δ'$-potentials supported on hypersurfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1012_4596 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | Spectral estimates for resolvent differences of self-adjoint elliptic operators Behrndt, Jussi Langer, Matthias Lotoreichik, Vladimir Spectral Theory Mathematical Physics Analysis of PDEs Functional Analysis Primary: 35P05, 35P20, Secondary: 47F05, 47L20, 81C15, 81Q10 The notion of quasi boundary triples and their Weyl functions is an abstract concept to treat spectral and boundary value problems for elliptic partial differential equations. In the present paper the abstract notion is further developed, and general theorems on resolvent differences belonging to operator ideals are proved. The results are applied to second order elliptic differential operators on bounded and exterior domains, and to partial differential operators with $δ$ and $δ'$-potentials supported on hypersurfaces. |
| title | Spectral estimates for resolvent differences of self-adjoint elliptic operators |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs Functional Analysis Primary: 35P05, 35P20, Secondary: 47F05, 47L20, 81C15, 81Q10 |
| url | https://arxiv.org/abs/1012.4596 |