Elliptic differential-operator with an abstract Robin boundary condition containing two spectral parameters, study in a non commutative framework
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866916953497534464 |
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| author | Favini, Angelo Labbas, Rabah Maingot, Stéphane Thorel, Alexandre |
| author_facet | Favini, Angelo Labbas, Rabah Maingot, Stéphane Thorel, Alexandre |
| contents | We study the solvability of boundary-value problems for differential-operator equations of the second order in L p (0, 1; X), with 1 < p < +$\infty$, X being a UMD complex Banach space. The originality of this work lies in the fact that we have considered the case when spectral complex parameters appear in the equation and in the abstract Robin boundary condition illustrated by some unbounded operator non commuting with the one used in the equation. Existence, uniqueness, representation formula, maximal regularity of the solution, sharp estimates and generation of strongly continuous analytic semigroup are proved. Many concrete applications are given for which our theory applies. This work gives news considerations with respect to all those studied by the authors in [7] and is a continuation, in some sense, of the results in [1] studied in Hilbertian spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_02744 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Elliptic differential-operator with an abstract Robin boundary condition containing two spectral parameters, study in a non commutative framework Favini, Angelo Labbas, Rabah Maingot, Stéphane Thorel, Alexandre Analysis of PDEs We study the solvability of boundary-value problems for differential-operator equations of the second order in L p (0, 1; X), with 1 < p < +$\infty$, X being a UMD complex Banach space. The originality of this work lies in the fact that we have considered the case when spectral complex parameters appear in the equation and in the abstract Robin boundary condition illustrated by some unbounded operator non commuting with the one used in the equation. Existence, uniqueness, representation formula, maximal regularity of the solution, sharp estimates and generation of strongly continuous analytic semigroup are proved. Many concrete applications are given for which our theory applies. This work gives news considerations with respect to all those studied by the authors in [7] and is a continuation, in some sense, of the results in [1] studied in Hilbertian spaces. |
| title | Elliptic differential-operator with an abstract Robin boundary condition containing two spectral parameters, study in a non commutative framework |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2111.02744 |