Conveners
Free Boundaries in Shape Optimization: MS-5-1
- Matteo Novaga (University of Pisa)
Free Boundaries in Shape Optimization: MS-5-2
- Giuseppe Buttazzo (University of Pisa)
Description
Organisers: Giuseppe Buttazzo, Matteo Novaga
-
Maria Stella Gelli (Università di Pisa Dipartimento di Matematica)08/09/2026, 10:30Free Boundaries in Shape Optimization
Starting from 2D lattice spin configurations satisfying the uniform state $\mathbf{e}_3$ outside a bounded domain $\Omega$, we investigate atomistic energies consisting of an exchange Heisenberg term together with an interfacial Dzyaloshinskii--Moriya interaction (DMI). In both discrete and continuum settings, imposing spatial confinement along with a topological constraint ($\text{degree}=1$)...
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Shokhrukh Kholmatov (University of Vienna)08/09/2026, 11:00Free Boundaries in Shape Optimization
We discuss regularity properties of Cartesian minimizers of the (anisotropic) area functional
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[
\int_a^b \Phi(-Du,1),dx+\int_a^b |u-g|^p,dx
]
defined on (BV(a,b)). We prove that if the (L^\infty)-norm of the forcing term (g) is sufficiently small, then every minimizer is locally Lipschitz continuous. Moreover, if the anisotropy (\Phi) is smooth and uniformly elliptic, then every minimizer... -
Cyrill Muratov (University of Pisa)08/09/2026, 11:30Free Boundaries in Shape Optimization
In this talk I will present our treatment of a geometric variational
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problem arising from modeling the equilibrium shapes of liquid drops
whose energy presents a competition of surface tension with the
repulsive Coulombic energy of a fixed number of point charges inside
the drop. The continuum analog of this problem in which the liquid is
treated as a perfect conductor is known to be... -
berardo ruffini (Università di Bologna)08/09/2026, 12:00Free Boundaries in Shape Optimization
We introduce a class of shape optimization problems modeled on Hartree type energies. From a shape optimization point of view, the energy is a sort of lower order perturbation of the first Dirichlet eigenvalue energy. We will partially discuss the existence and rigidity of optimizer in certain regimes and focus on the nonexistence issue in other regimes. The short talk is based on ongoing...
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Luca Briani (Technische Universität München)08/09/2026, 16:30Free Boundaries in Shape Optimization
We present a variational definition of the essential spectrum suitable for nonlinear operators such as the Dirichlet p-Laplacian and discuss an extension of Persson's theorem to this framework. Finally, we show that the Ljusternik-Schnirelmann minmax levels of the constrained p-Dirichlet integral are attained whenever one of these levels is below Persson's threshold. This is based on joint...
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Maria del Mar Gonzalez Nogueras (Universidad Autonoma de Madrid)08/09/2026, 17:00Free Boundaries in Shape Optimization
Motivated by the study of the Paneitz operator in geometry, we consider eigenvalue problems for some fourth-order problems, with a particular emphasis on eigenvalue bounds and shape optimization.
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Mickaël Nahon (Université Grenoble Alpes)08/09/2026, 17:30Free Boundaries in Shape Optimization
Consider the following functional
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$$u\in H^2(D,\mathbb{R})\mapsto\int_D(|\nabla^2 u|^2+\chi_{u\neq 0})$$ where $D\subset \mathbb{R}^2$. This is a higher order analogue of the Alt-Caffarelli problem, and its local minimizers are linked to several shape optimization question: primarily with the minimization (under area constraint) of the critical buckling load of a clamped plate... -
Nicolas Van Goethem (Universidade de Lisboa)08/09/2026, 18:00Free Boundaries in Shape Optimization
We propose a mechanism for the onset of polygonization in crystals with dislocations. Starting from a diffuse distribution, we show that the interaction between elasticity and dislocation motion can destabilize the homogeneous state. The classical Peach–Koehler force tends to stabilize this state, while a non-local Beltrami contribution drives the instability.
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The fastest-growing structures...