We prove that the Robin ground state and the Robin torsion function are respectively log-concave and 1/2 -concave on an uniformly convex domain Ω⊂RN of class Cm, 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; Fragalà, Ilaria. - In: CAMBRIDGE JOURNAL OF MATHEMATICS. - ISSN 2168-0930. - 9:1(2021), pp. 177-212. [10.4310/CJM.2021.v9.n1.a3]
Concavity properties of solutions to Robin problems
Crasta, Graziano;
2021
Abstract
We prove that the Robin ground state and the Robin torsion function are respectively log-concave and 1/2 -concave on an uniformly convex domain Ω⊂RN of class Cm, 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 allegati a questo prodotto
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