33 citations · 84 across the 23 of their papers we have counts for
24 papers
A discrete-time overdetermined problem for the heat equation
Lorenzo Cavallina, Andrea Pinamonti
In this paper, we consider a parabolic counterpart of Serrin's overdetermined problem, in which the overdetermined condition (constant flux condition) is imposed only on a discrete…
Elliptic and parabolic overdetermined problems in multi-phase settings
Lorenzo Cavallina, Giorgio Poggesi
The present paper provides symmetry results for a class of overdetermined problems of elliptic and parabolic type in multi-phase settings, including various extensions of remarkabl…
A miscellanea of qualitative and symmetry properties of the solutions to the two-phase Serrin's problem
Lorenzo Cavallina
This paper investigates the solutions to the two-phase Serrin's problem, an overdetermined boundary value problem motivated by shape optimization. Specifically, we study the torsio…
Visualizing Shape Functionals via Sinkhorn Multidimensional Scaling
Toshiaki Yachimura, Jun Okamoto, Lorenzo Cavallina
In this paper, we present Sinkhorn multidimensional scaling (Sinkhorn MDS) as a method for visualizing shape functionals in shape spaces. This approach uses the Sinkhorn divergence…
Two extremum problems for Neumann eigenvalues
Lorenzo Cavallina, Kei Funano, Antoine Henrot +3
Neumann eigenvalues being non-decreasing with respect to domain inclusion, it makes sense to study the two shape optimization problems $\min\{μ_k(Ω):Ω\mbox{ convex},Ω\subset D, \}$…
Face 2-phase: how much overdetermination is enough to get symmetry in two-phase problems
Lorenzo Cavallina, Giorgio Poggesi
We provide a full characterization of multi-phase problems under a large class of overdetermined Serrin-type conditions. Our analysis includes both symmetry and asymmetry (includin…
Pythagorean Theorem, Law of Sines and Law of Cosines: alternative proofs via shape derivatives
Lorenzo Cavallina
We provide an alternative unified approach for proving the Pythagorean theorem (in dimension and higher), the law of sines and the law of cosines, based on the concept of shape…
Symmetry and asymmetry in a multi-phase overdetermined problem
Lorenzo Cavallina
A celebrated theorem of Serrin asserts that one overdetermined condition on the boundary is enough to obtain radial symmetry in the so-called one-phase overdetermined torsion probl…
Why are the solutions to overdetermined problems usually "as symmetric as possible"?
Lorenzo Cavallina
In this paper, we study the symmetry properties of nondegenerate critical points of shape functionals using the implicit function theorem. We show that, if a shape functional is in…
How to construct parametrized families of free boundaries near nondegenerate solutions
Lorenzo Cavallina
In this paper, we introduce the notion of variational free boundary problem. Namely, we say that a free boundary problem is variational if its solutions can be characterized as the…
Quantitative stability estimates for a two-phase Serrin-type overdetermined problem
Lorenzo Cavallina, Giorgio Poggesi, Toshiaki Yachimura
In this paper, we deal with an overdetermined problem of Serrin-type with respect to a two-phase elliptic operator in divergence form with piecewise constant coefficients. In parti…
The simultaneous asymmetric perturbation method for overdetermined free boundary problems
Lorenzo Cavallina
In this paper, we introduce a new method for applying the implicit function theorem to find nontrivial solutions to overdetermined problems with a fixed boundary (given) and a free…
Local analysis of a two phase free boundary problem concerning mean curvature
Lorenzo Cavallina
We consider an overdetermined problem for a two phase elliptic operator in divergence form with piecewise constant coefficients. We look for domains such that the solution of a…
The double queen Dido's problem
Lorenzo Cavallina, Antoine Henrot, Shigeru Sakaguchi
This paper deals with a variation of the classical isoperimetric problem in dimension for a two-phase piecewise constant density whose discontinuity interface is a given h…
Symmetry breaking solutions for a two-phase overdetermined problem of Serrin-type
Lorenzo Cavallina, Toshiaki Yachimura
In this paper, we consider an overdetermined problem of Serrin-type for a two-phase elliptic operator with piecewise constant coefficients. We show the existence of infinitely many…
A characterization of a hyperplane in two-phase heat conductors
Lorenzo Cavallina, Shigeru Sakaguchi, Seiichi Udagawa
We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities, where initially one has…
Analysis of two-phase shape optimization problems by means of shape derivatives
Lorenzo Cavallina
This is my Ph.D. Thesis at Tohoku Univeristy (July 2018). It presents the theory on shape derivatives and focuses on its applications to two-phase optimization problems. In particu…
The homogenization method for topology optimization of structures: old and new
Grégoire Allaire, Lorenzo Cavallina, Nobuhito Miyake +2
These are the lecture notes of a short course on the homogenization method for topology optimization of structures, given by Grégoire Allaire, during the "GSIS International Summer…
On a two-phase Serrin-type problem and its numerical computation
Lorenzo Cavallina, Toshiaki Yachimura
We consider an overdetermined problem of Serrin-type with respect to an operator in divergence form with piecewise constant coefficients. We give sufficient condition for unique so…
Stability analysis of the two-phase torsional rigidity near a radial configuration
Lorenzo Cavallina
Let denote the unit ball of () centered at the origin. We suppose that contains a core, given by a smaller concentric ball , made of a (poss…
Two-phase heat conductors with a surface of the constant flow property
Lorenzo Cavallina, Rolando Magnanini, Shigeru Sakaguchi
We consider a two-phase heat conductor in with consisting of a core and a shell with different constant conductivities. We study the role played by radial…
Locally optimal configurations for the two-phase torsion problem in the ball
Lorenzo Cavallina
We consider the unit ball () filled with two materials with different conductivities. We perform shape derivatives up to the second order to find out…
Non-trivial translation-invariant valuations on
Lorenzo Cavallina
Translation-invariant valuations on the space are examined. We prove that such functionals vanish on functions with compact support. Moreover a rich family…
Monotone valuations on the space of convex functions
L. Cavallina, A. Colesanti
We consider the space of convex functions defined in the Euclidean -dimensional space, which are lower semi-continuous and tend to infinity at infinity. We study real-valued val…