Shape Optimization and Isoperimetric and Functional Inequalities
November 21 – 25, 2016
The main purpose of the workshop is to bring together specialists working on various topics involving geometric inequalities, isoperimetric and functional inequalities, partial differential equations on variable domains, with particular attention to the dependence of the solutions of the state equations (generally partial differential equations) on the geometry of their domain of definition. Precisely, we will involve specialists on – shape optimization problems, – free boundary problems, – spectral analysis and geometrical properties – isoperimetric inequalities and other geometric or functional inequalities. The main goal of the workshop is to make the point on some recent techniques, mainly of variational type, which have been developed to prove the existence of optimal shapes and to study their regularity. A second main issue is to present the state of the art on some celebrated open problems and conjectures, and try to make a step forward in the direction of solving them, or at least to obtain new partial information.
Scientific & Organizing Committee

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


  • 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

  • Pedro Freitas (University of Lisbon)

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