On the inverse of the sum of two sectorial operators
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2012
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| _version_ | 1866916168468529152 |
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| author | Roidos, Nikolaos |
| author_facet | Roidos, Nikolaos |
| contents | We study an abstract linear operator equation on a Banach space by using the inverse of the sum of two sectorial operators. We prove that the boundedness of a special type of operator valued $H^\infty$-calculus is sufficient for maximal regularity of the solution. We apply the result to the abstract parabolic problem, to give a maximal $L^{p}$-regularity condition. We also study the abstract hyperbolic problem and give a sufficient condition for the existence of solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1207_0749 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | On the inverse of the sum of two sectorial operators Roidos, Nikolaos Functional Analysis Analysis of PDEs 47A50, 35K90, 35L90 We study an abstract linear operator equation on a Banach space by using the inverse of the sum of two sectorial operators. We prove that the boundedness of a special type of operator valued $H^\infty$-calculus is sufficient for maximal regularity of the solution. We apply the result to the abstract parabolic problem, to give a maximal $L^{p}$-regularity condition. We also study the abstract hyperbolic problem and give a sufficient condition for the existence of solution. |
| title | On the inverse of the sum of two sectorial operators |
| topic | Functional Analysis Analysis of PDEs 47A50, 35K90, 35L90 |
| url | https://arxiv.org/abs/1207.0749 |