Robin boundary condition on scale irregular fractals

Capitanelli, Raffaela

doi:10.3934/cpaa.2010.9.1221

Cited by 17 publications

(27 citation statements)

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“…Finally, for the second term on the right-hand side in (18) we use Theorem 2.1 in [9] (see also Lemma 8.4 in [12]): so, we obtain that…”

Section: Theorem 35 Letmentioning

confidence: 98%

“…It is a particular case of extension theorem due to Jones (Theorem 1 in [13]) as the domains Ω (ξ ),n are (ε, ∞) domains with ε independent of n (for the proof, see [9]). …”

Section: Trace and Extensions Theoremsmentioning

confidence: 99%

“…Recently, Robin Problems on fractal domains have been studied (see [7][8][9], and the references therein).…”

Section: Robin Problemmentioning

confidence: 99%

“…In Section 4 we need a theorem that extends functions of the fractional Sobolev spaces H σ (Ω (ξ ) ) with 1 2 < σ 1, to the fractional Sobolev spaces H σ (R 2 ) (for the proof, see [9]). …”

Section: Theorem 33 For Any N ∈ N There Exists a Bounded Linear Exmentioning

confidence: 99%

“…The study of reinforcement problems on domains with fractal boundaries is recent (see [19,20]) and, to our knowledge, our approach to Robin Problems on fractal domains in the framework of insulating layers is new. This work is inspired by recent papers dealing with fractal homogenization (see [19,20]) and with Robin Problem on fractal domains (see [7][8][9]). …”

Section: Introductionmentioning

confidence: 98%

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Insulating layers and Robin Problems on Koch mixtures

Capitanelli

Vivaldi

2011

Journal of Differential Equations

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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

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“…Finally, for the second term on the right-hand side in (18) we use Theorem 2.1 in [9] (see also Lemma 8.4 in [12]): so, we obtain that…”

Section: Theorem 35 Letmentioning

confidence: 98%

“…It is a particular case of extension theorem due to Jones (Theorem 1 in [13]) as the domains Ω (ξ ),n are (ε, ∞) domains with ε independent of n (for the proof, see [9]). …”

Section: Trace and Extensions Theoremsmentioning

confidence: 99%

“…Recently, Robin Problems on fractal domains have been studied (see [7][8][9], and the references therein).…”

Section: Robin Problemmentioning

confidence: 99%

Section: Theorem 33 For Any N ∈ N There Exists a Bounded Linear Exmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Insulating layers and Robin Problems on Koch mixtures

Capitanelli

Vivaldi

2011

Journal of Differential Equations

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Fractional Cauchy problem on random snowflakes

Capitanelli

D’Ovidio

2021

J. Evol. Equ.

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We consider time-changed Brownian motions on random Koch (pre-fractal and fractal) domains where the time change is given by the inverse to a subordinator. In particular, we study the fractional Cauchy problem with Robin condition on the pre-fractal boundary obtaining asymptotic results for the corresponding fractional diffusions with Robin, Neumann and Dirichlet boundary conditions on the fractal domain.

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