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Ainsi, tout mathématicien intéressé par l’optimisation de forme, les problèmes à frontière libre, la géométrie spectrale est le bienvenu. Durant ce colloque, nous ferons le point sur les méthodes et idées récentes, principalement de nature variationnelle, qui ont été développées pour prouver l’existence de solutions et étudier leur régularité. Il sera également présenté un état de l’art pour plusieurs problèmes et conjectures célèbres et les dernières avancées pour les résoudre ou mieux les comprendre.

Dorin Bucur (Université de Savoie Mont-Blanc)
Giuseppe Buttazzo (University of Pisa)
Antoine Henrot (Université de Lorraine)
Aldo Pratelli (Erlangen-Nürnberg University)

• José M. Arrieta (Complutense University of Madrid)

Thin domains with a locally periodic highly oscillatory boundary

• Mark Ashbaugh (University of Missouri)

A Sharp Lower Bound for the First Eigenvalue of the Vibrating Clamped Plate under Compression

• Catherine Bandle (University of Basel) and Alfred Wagner ( RWTH Aachen)

On an eigenvalue problem with infinitely many positive and negative eigenvalues: Rayleigh-Faber-Krahn inequalities for the principal eigenvalues

• Rafael Benguria ( P. U. Catolica de Chile)

The Brezis-Nirenberg Problem for the Laplacian with a singular drift in Rn and also in Sn

• Chiara Bianchini (University of Florence)

Wulff Shape characterization for anisotropic capacitary potentials

• Virginie Bonnaillie-Noel (ENS Paris)

Spectral minimal partitions for a family of tori

• Friedemann Brock (University of Rostock)

Some isoperimetric inequalities onRN with respect to weights x alpha

• Bruno Colbois (Université de Neuchâtel)

Bounds for the spectrum of the magnetic Laplacian

• Gisella Croce (Université Le Havre Normandie)

On the selection of solutions to a nonlinear PDE system

• Gianni Dal Maso (SISSA, Trieste)

Existence and uniqueness of dynamic evolutions for a peeling test in dimension one

• Marc Dambrine (Université de Pau)

Taking uncertainties into account in numerical shape optimization

• Guido De Philippis (SISSA Trieste)

Allard’s rectifiability theorem for anisotropic energies

• Ilaria Fragalà (Politecnico di Milano)

Some new inequalities for the Cheeger constant

Asymptotic behaviour of optimisers of Laplace eigenvalues

• Nicola Fusco (University of Naples Federico II)

A stability result for the first eigenvalue of the p-Laplacian

• Filippo Gazzola (Politecnico di Milano)

A minimaxmax problem for improving the torsional stabilityof rectangular plates

• Alessandro Giacomini (University of Brescia)

Shape optimization with Robin conditions and freediscontinuity problems

• Alexandre Girouard ( Université de Laval)

Discretization and Steklov eigenvalues of compact manifold with boundary

• Katie Gittins (Université de Neuchâtel)

Asymptotic optimal sets for the eigenvalues of the Laplacian

• Bernd Kawohl (University of Köln)

Two dimensions are easier

• David Krejcirik (Nuclear Physics Institute ASCR)

Isoperimetric versus isochoric spectral optimisation for theRobin problem

• Jimmy Lamboley (Université Paris-Dauphine)

Regularity for functionals involving perimeter

• Richard Laugesen (University of Illinois)

Optimal stretching for lattice points and eigenvalues

• Dario Mazzoleni ( University of Turin)

Regularity of the optimal sets for spectral functionals
Part II, some generalizations

• Frank Morgan (Williams College,  USA)

Isoperimetry with Density

• Nikolai Nadirashvili ( Aix-Marseille Université)

Isoperimetric inequalities for spectrum of Laplacian on surfaces

• Carlo Nitsch (University of Naples Federico II)

Symmetry breaking for a problem in optimal insulation

• Edouard Oudet (Université Grenoble Alpes)

Convex relaxation and variational approximation of the Euclidean Steiner

• Iosif Polterovich (Université de Montréal)

Nodal geometry of Steklov eigenfunctions

• Yannick Privat (Université Pierre et Marie Curie)

Geometrical properties of resources optimal arrangements for species survival

• Paolo Salani (University of Florence)

About the stability of Borell-Brascamp-Lieb inequalities

• Kathrin Stollenwerk (RWTH Aachen University)

Optimal shape of a domain which minimizes the buckling load of a clamped plate

• Susanna Terracini (University of Turin)

Regularity of the optimal sets for spectral functionals
Part I: sum of eigenvalues.

• Cristina Trombetti (University of Naples Federico II)

On the Stability of the Bossel-Daners Inequality

• Michiel van den Berg (University of Bristol)

On Polya inequality for torsional rigidity and firstDirichlet eigenvalue

• Bozhidar Velichkov ( Université Grenoble Alpes

An epi-perimetric inequality approach to the regularity of the free boundaries