This paper deals with a reinforcement problem for a plane domain Omega((xi)) whose boundary is a deterministic or random "mixture" of self-similar Koch curves. We construct an epsilon-thin polygonal 2-dimensional fiber Sigma((xi),n)(epsilon), n is an element of N, 0 < epsilon < 1, around pre-fractal approximating domains Omega((xi),n) and related suitable energy functionals. The aim of this paper is to study the asymptotic behavior of the reinforced energy functionals while, simultaneously, the thickness of the fibers and the conductivity of the functionals on the fibers converges to 0 as n -> +infinity. (C) 2011 Elsevier Inc. All rights reserved.
Insulating layers and Robin Problems on Koch mixtures / Capitanelli, Raffaela; Vivaldi, Maria Agostina. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 251:4-5(2011), pp. 1332-1353. [10.1016/j.jde.2011.02.003]
Insulating layers and Robin Problems on Koch mixtures
CAPITANELLI, Raffaela;VIVALDI, Maria Agostina
2011
Abstract
This paper deals with a reinforcement problem for a plane domain Omega((xi)) whose boundary is a deterministic or random "mixture" of self-similar Koch curves. We construct an epsilon-thin polygonal 2-dimensional fiber Sigma((xi),n)(epsilon), n is an element of N, 0 < epsilon < 1, around pre-fractal approximating domains Omega((xi),n) and related suitable energy functionals. The aim of this paper is to study the asymptotic behavior of the reinforced energy functionals while, simultaneously, the thickness of the fibers and the conductivity of the functionals on the fibers converges to 0 as n -> +infinity. (C) 2011 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
