Motion of three-dimensional elastic films by anisotropic surface diffusion with curvature regularization

Fonseca, Irene; Fusco, Nicola; Leoni, Giovanni; Morini, Massimiliano

doi:10.2140/apde.2015.8.373

Cited by 16 publications

(20 citation statements)

References 30 publications

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“…We stress that this cannot be obtained by some general existence results, but is achieved through a very careful construction (pp. [28][29][30][31][32][33][34][35][36], that follows only partially the analogous one in [18]. We believe that the construction in [18] could indeed be improved by adopting an approach similar to ours, in order to take also some pathological situations into account.…”

Section: Introductionmentioning

confidence: 89%

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Equilibrium Configurations for Epitaxially Strained Films and Material Voids in Three-Dimensional Linear Elasticity

Crismale

Friedrich

2020

Arch Rational Mech Anal

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We extend the results about existence of minimizers, relaxation, and approximation proven by Chambolle et al. in 2002 and for an energy related to epitaxially strained crystalline films, and by Braides, Chambolle, and Solci in 2007 for a class of energies defined on pairs of function-set. We study these models in the framework of three-dimensional linear elasticity, where a major obstacle to overcome is the lack of any a priori assumption on the integrability properties of displacements. As a key tool for the proofs, we introduce a new notion of convergence for (d−1)-rectifiable sets that are jumps of GSBD p functions, called σ p sym -convergence.2010 Mathematics Subject Classification. 49Q20, 26A45, 49J45, 74G65.

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Section: Introductionmentioning

confidence: 89%

“…Let us stress that in this work we consider exclusively a static setting. For evolutionary models, we mention the recent works [32,39,40,51].…”

Section: Introductionmentioning

confidence: 99%

Equilibrium Configurations for Epitaxially Strained Films and Material Voids in Three-Dimensional Linear Elasticity

Crismale

Friedrich

2020

Arch Rational Mech Anal

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“…Only recently, first analytic results for the highly non-linear sixth-order partial differential Equations (1)- (3) (including corner rounding regularization) have been obtained [125,126]. Most numerical treatments consider only specific aspects of the whole problem.…”

Section: Comparison Of Computational Approachesmentioning

confidence: 99%

Continuum modelling of semiconductor heteroepitaxy: an applied perspective

Bergamaschini

Salvalaglio

Backofen

et al. 2016

Advances in Physics: X

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Semiconductor heteroepitaxy involves a wealth of qualitatively different, competing phenomena. Examples include threedimensional island formation, injection of dislocations, mixing between film and substrate atoms. Their relative importance depends on the specific growth conditions, giving rise to a very complex scenario. The need for an optimal control over heteroepitaxial films and/or nanostructures is widespread: semiconductor epitaxy by molecular beam epitaxy or chemical vapour deposition is nowadays exploited also in industrial environments. Simulation models can be precious in limiting the parameter space to be sampled while aiming at films/nanostructures with the desired properties. In order to be appealing (and useful) to an applied audience, such models must yield predictions directly comparable with experimental data. This implies matching typical time scales and sizes, while offering a satisfactory description of the main physical driving forces. It is the aim of the present review to show that continuum models of semiconductor heteroepitaxy evolved significantly, providing a promising tool (even a working tool, in some cases) to comply with the above requirements. Several examples, spanning from the nanometre to the micron scale, are illustrated. Current limitations and future research directions are also discussed.

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“…We conclude this introduction by mentioning that it would be interesting to investigate whether the flow (1.5) studied in [23] converge to (1.3) as ε → 0 + . This issue could be probably addressed by adapting the methods developed in [7].…”

Section: Introductionmentioning

confidence: 99%

“…Here K ∂Ft stands for the Gaussian curvature of ∂F t , ε > 0 is a small parameter, and p > 2. The local-intime existence and the asymptotic stability results proven in [23] (see also [22,39]) rely heavily on the presence of the curvature regularization, which makes the elastic contribution a lower order term easily controlled by the sixth order leading terms of the equation. In fact, all the estimates provided there are ε-dependent and degenerate as ε → 0 + .…”

Section: Introductionmentioning

confidence: 99%