Regularity Theory for Free Boundary and Geometric Variational Problems

Levico Terme, 5-10 September 2021


Centro Internazionale di Ricerca Matematica - Fondazione Bruno Kessler

ERC VaReg (European Union - Horizon 2020)


     This workshop is dedicated to the recent advances in the theories of

Free Boundary Problems and Minimal Surfaces

which include problems and combine tools from different fields as for instance PDEs, Calculus of Variations and Geometric Analysis.

The main topic is the regularity and the fine structure of geometric objects (free boundaries, minimal surfaces, free interfaces) obtained trough the minimization of variational functionals. The description of the local structure of these minima is a common objective for both the fields of Free Boundary Problems and Minimal Surfaces and the techniques developed in this context have found application to problems from different areas.

The workshop brings together young researchers and leading experts in these fields, the focus being on the recent important breakthroughs in the regularity of the free boundaries and minimal surfaces, in particular, on questions related to the formation and the structure of singularities. 


Susanna Terracini (Università di Torino)

Yannick Sire (Johns Hopkins University)

Alessio Figalli* (ETH Zürich)

Dorin Bucur (Université de Savoie)

Matteo Focardi (Università di Firenze)

Jonas Hirsch (Universität Leipzig)

Andrea Mondino* (University of Oxford)

Annalisa Massaccesi (Università di Padova)

Andrea Marchese (Università di Trento)

Neshan Wickramasekera* (University of Cambridge)

Connor Mooney (UC Irvine)

Robin Neumayer (Carnegie Mellon)

Nicola Soave (Politecnico di Milano)

Stefano Vita (Università di Milano-Bicocca)

Dario Mazzoleni (Università di Pavia)

Xavier Ros-Oton* (Universitat de Barcelona)

Zihui Zhao (University of Chicago)

Domenico Angelo La Manna (University of Jyväskylä)

Xavier Fernandez-Real (EPFL - Lausanne)

Giorgio Tortone (Università di Pisa)

Serena Guarino Lo Bianco* (University of Naples)

Ekaterina Mukoseeva (University of Helsinki)

Mickael Nahon (Université de Savoie)

Simone Steinbrüchel* (Universität Leipzig)

Francesco Paolo Maiale (Scuola Normale Superiore)

Nicolò Forcillo (Unversità di Bologna)

Alessandro Audrito (ETH Zürich)

Joseph Feneuil (Università di Pisa)

Riccardo Tione (EPFL - Lausanne)

Luca Spolaor (University of California San Diego)

Bozhidar Velichkov (Università di Pisa)

* = remote participation


Monday 6 Sept

09:00-09:50   Susanna Terracini

Free boundaries in segregation problems

10:10-11:00   Andrea Marchese

Area minimizing currents mod p: general regularity theory

11:40-12:30   Connor Mooney

The Bernstein problem for equations of minimal surface type

15:00-15:50   Alessandro Audrito

Interface regularity and 1D symmetry for semilinear one-phase problem

16:10-17:00   Giorgio Tortone

The capillarity one-phase problem

Tuesday 7 Sept

09:00-09:50   Andrea Mondino

Optimal transport, weak Laplacian bounds and minimal boundaries
in non-smooth spaces with lower Ricci curvature bounds

10:10-11:00   Alessio Figalli

Generic regularity in obstacle problems

11:40-12:30   Domenico Angelo La Manna

Charged liquid drop

15:00-15:50   Stefano Vita

Strong unique continuation and local asymptotics
at the boundary for fractional elliptic equations

16:10-17:00   Nicolò Forcillo

A perturbative estimates approach to the free boundary regularity
in the one-phase Stefan problem

Wednesday 8 Sept

09:00-09:50   Xavier Ros-Oton

Stable cones in the thin one-phase free boundary problem

10:10-11:00   Jonas Hirsch

Area minimizing hypersurfaces mod(p): A geometric free boundary problem

11:40-12:30   Annalisa Massaccesi

Frobenius theorem for weak submanifolds

Thursday 9 Sept

09:00-09:50   Dorin Bucur

Multiphase free discontinuity problems: monotonicity formula and regularity results

10:10-11:00   Dario Mazzoleni

A spectral shape optimization problem with a nonlocal competing term

11:40-12:30   Robin Neumayer

Quantitative Faber-Krahn inequalities and the ACF Monotonicity Formula

15:00-15:50   Yannick Sire

Some results on harmonic maps with free boundary and beyond

16:10-17:00   Simone Steinbrüchel

Boundary regularity for higher multiplicity boundaries of 2D area minimizing currents

Friday 10 Sept

09:00-09:50   Nicola Soave

Free boundary problems in the spatial segregation of some competing systems

10:10-11:00   Zihui Zhao

Boundary unique continuation of Dini domains

11:40-12:30   Matteo Focardi

On the regularity of singular sets of minimizers for the Mumford-Shah energy


Book of abstracts

Scientific organizers: Luca Spolaor and Bozhidar Velichkov

Organizers: Augusto Micheletti (University of Trento), Francesca Menconi (University of Pisa)

Contacts: bozhidar.velichkov[at], lspolaor[at], augusto.micheletti[at], francesca.menconi[at]