dc.contributor.author Lamboley, Jimmy HAL ID: 6598 dc.date.accessioned 2010-11-02T15:23:23Z dc.date.available 2010-11-02T15:23:23Z dc.date.issued 2011 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/4982 dc.language.iso en en dc.subject overdetermined boundary value problems en dc.subject convex constraint en dc.subject eigenvalues of the Laplacian en dc.subject shape optimization en dc.subject conformal map en dc.subject regularity of free boundaries en dc.subject.ddc 515 en dc.title About Hölder-regularity of the convex shape minimizing λ2 en dc.type Article accepté pour publication ou publié dc.description.abstracten In this paper, we consider the well-known following shape optimization problem: $$\lambda_2(\Omega^*)=\min_{\stackrel{|\Omega|=V_0} {\Omega\textrm{ convex}}} \lambda_2(\Omega),$$ where $\lambda_2(\Om)$ denotes the second eigenvalue of the Laplace operator with homogeneous Dirichlet boundary conditions in $\Om\subset\R^2$, and $|\Om|$ is the area of $\Om$. We prove, under some technical assumptions, that any optimal shape $\Omega^*$ is $\mathcal{C}^{1,\frac{1}{2}}$ and is not $\C^{1,\alpha}$ for any $\alpha>\frac{1}{2}$. We also derive from our strategy some more general regularity results, in the framework of partially overdetermined boundary value problems, and we apply these results to some other shape optimization problems. en dc.relation.isversionofjnlname Applicable Analysis dc.relation.isversionofjnlvol 90 dc.relation.isversionofjnlissue 2 dc.relation.isversionofjnldate 2011 dc.relation.isversionofjnlpages 263-278 dc.relation.isversionofdoi http://dx.doi.org/10.1080/00036811.2010.496361 dc.identifier.urlsite http://hal.archives-ouvertes.fr/hal-00530272/fr/ en dc.description.sponsorshipprivate oui en dc.relation.isversionofjnlpublisher Taylor and Francis en dc.subject.ddclabel Analyse en
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