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dc.contributor.authorLamboley, Jimmy
HAL ID: 6598
dc.date.accessioned2010-11-02T15:23:23Z
dc.date.available2010-11-02T15:23:23Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/4982
dc.language.isoenen
dc.subjectoverdetermined boundary value problemsen
dc.subjectconvex constrainten
dc.subjecteigenvalues of the Laplacianen
dc.subjectshape optimizationen
dc.subjectconformal mapen
dc.subjectregularity of free boundariesen
dc.subject.ddc515en
dc.titleAbout Hölder-regularity of the convex shape minimizing λ2en
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn 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.isversionofjnlnameApplicable Analysis
dc.relation.isversionofjnlvol90
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2011
dc.relation.isversionofjnlpages263-278
dc.relation.isversionofdoihttp://dx.doi.org/10.1080/00036811.2010.496361
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00530272/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherTaylor and Francisen
dc.subject.ddclabelAnalyseen


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