2015 **Abstract:** It is well-known from the recent literature that nonlocal integral models are suitable to approximate integral functionals or partial differential equations. In the present work, a nonlocal optimal design model has been considered as approximation of the corresponding classical or local optimal control problem. The new model is driven by a nonlocal elliptic equation and the cost functional belongs to a broad class of nonlocal functional integrals. The purpose of this paper is to prove existence of optimal desi…

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(18 citation statements)

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“…This result generalizes, giving a simpler proof, previous results for a related nonlocal situation in the linear case [3,Th. 6].…”

supporting

confidence: 87%

“…This result generalizes, giving a simpler proof, previous results for a related nonlocal situation in the linear case [3,Th. 6].…”

supporting

confidence: 87%

“…All details for the derivation of these achievements can be found at papers. 30,31,38,42,43 The main result of this paper is the existence of nonlocal optimal design (Theorem 4). The proof in given in Section 3.…”

confidence: 99%

“…[23][24][25][26][27][28][29] However, there is not much literature concerning nonlocal optimal design models. We refer, among others, Andrés and Muñoz, 30,31 Bonder and Spedaletti, 32 D'Elia and Gunzburger, 33,34 and Zhou and Du 35,36 mainly in the context of elliptic equations. Also, Bonder et al 37 is a valuable paper, where an H-convergence study has been carried out.…”

confidence: 99%

“…where Ω ⊂ R n is an open subset, u : Ω → R d is in some Lebesgue space L p , and the integrand w : Ω × Ω × R d × R d → R ∪ {∞} has some measurability and continuity properties. This kind of functionals appears in many contexts in the mathematical modelling of some processes, whose common feature is their nonlocal nature; we mention here micromagnetics [38], phase transitions [4], peridynamics [39], pattern formation [25], image processing [27], population dispersal [20], diffusion [8] and optimal design [5]. It also has applications in the characterization of Sobolev spaces [16].…”

mentioning

confidence: 99%

“…Boundary conditions, coercivity and existence of minimizers. In this section we give conditions for the existence of minimizers of (5) I :…”

mentioning

confidence: 99%