Full metadata record
| DC pole | Hodnota | Jazyk |
|---|---|---|
| dc.contributor.author | Bobkov, Vladimír | |
| dc.contributor.author | Kolonitskii, Sergey | |
| dc.date.accessioned | 2020-11-02T11:00:18Z | |
| dc.date.available | 2020-11-02T11:00:18Z | |
| dc.date.issued | 2020 | |
| dc.identifier.citation | BOBKOV, V., KOLONITSKII, S. Second-order derivative of domain-dependent functionals along Nehari manifold trajectories. ESAIM-Control optimisation and calculus of variations, 2020, roč. 26, č. 48, s. 1-29. ISSN 1292-8119. | en |
| dc.identifier.issn | 1292-8119 | |
| dc.identifier.uri | 2-s2.0-85091818874 | |
| dc.identifier.uri | http://hdl.handle.net/11025/39877 | |
| dc.format | 29 s. | cs |
| dc.format.mimetype | application/pdf | |
| dc.language.iso | en | en |
| dc.publisher | EDP Sciences | en |
| dc.relation.ispartofseries | Esaim-control Optimisation And Calculus Of Variations | en |
| dc.rights | © EDP Sciences | en |
| dc.rights | Plný text není přístupný. | en |
| dc.title | Second-order derivative of domain-dependent functionals along Nehari manifold trajectories | en |
| dc.type | článek | cs |
| dc.type | article | en |
| dc.rights.access | closedAccess | en |
| dc.type.version | publishedVersion | en |
| dc.description.abstract-translated | Assume that a family of domain-dependent functionals EΩt possesses a corresponding family of least energy critical points ut which can be found as (possibly nonunique) minimizers of EΩt over the associated Nehari manifold N(Ωt). We obtain a formula for the second-order derivative of EΩt with respect to t along Nehari manifold trajectories of the form αt(u0(Φt−1(y)) + tv(Φt−1(y))), y ∈ Ωt, where Φt is a diffeomorphism such that Φt(Ω0) = Ωt, αt ∈ ℝ is a N(Ωt)-normalization coefficient, and v is a corrector function whose choice is fairly general. Since EΩt [ut] is not necessarily twice differentiable with respect to t due to the possible nonuniqueness of ut, the obtained formula represents an upper bound for the corresponding second superdifferential, thereby providing a convenient way to study various domain optimization problems related to EΩt. An analogous formula is also obtained for the first eigenvalue of the p-Laplacian. As an application of our results, we investigate the behaviour of the first eigenvalue of the Laplacian with respect to particular perturbations of rectangles. | en |
| dc.subject.translated | Shape Hessian | en |
| dc.subject.translated | second-order shape derivative | en |
| dc.subject.translated | domain derivative | en |
| dc.subject.translated | Hadamard formula | en |
| dc.subject.translated | perturbation of boundary | en |
| dc.subject.translated | superlinear nonlinearity | en |
| dc.subject.translated | Nehari manifold | en |
| dc.subject.translated | least energy solution | en |
| dc.subject.translated | first eigenvalue | en |
| dc.identifier.doi | 10.1051/cocv/2019053 | |
| dc.type.status | Peer-reviewed | en |
| dc.identifier.document-number | 568562000005 | |
| dc.identifier.obd | 43930289 | |
| dc.project.ID | LO1506/PUNTIS - Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnost | cs |
| dc.project.ID | GA18-03253S/Diferenciální rovnice se speciálními typy nelinearit | cs |
| Vyskytuje se v kolekcích: | Články / Articles (NTIS) OBD | |
Soubory připojené k záznamu:
| Soubor | Velikost | Formát | |
|---|---|---|---|
| BobkovKolonitskii_SecondDerivative_2020_published.pdf | 699,56 kB | Adobe PDF | Zobrazit/otevřít Vyžádat kopii |
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