33 citations · 84 across the 23 of their papers we have counts for
4 papers · 1 filter
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…