We prove that the Robin ground state and the Robin torsion function are respectively log-concave and1/2-concave on an uniformly convex domain Ω ⊂ ℝ^N of class C^m, with [m –N/2 ] ≥ 4, provided the Robin parameter exceeds a critical threshold. Such threshold depends on N, m, and on the geometry of Ω, precisely on the diameter and on the boundary curvatures up to order m.
Concavity properties of solutions to Robin problems
Crasta, Graziano;Fragala', Ilaria
2021-01-01
Abstract
We prove that the Robin ground state and the Robin torsion function are respectively log-concave and1/2-concave on an uniformly convex domain Ω ⊂ ℝ^N of class C^m, with [m –N/2 ] ≥ 4, provided the Robin parameter exceeds a critical threshold. Such threshold depends on N, m, and on the geometry of Ω, precisely on the diameter and on the boundary curvatures up to order m.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
11311-1203466_Crasta.pdf
accesso aperto
:
Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione
340.88 kB
Formato
Adobe PDF
|
340.88 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
