On the energy functionals derived from a non-homogeneous p-Laplacian equation: Γ-convergence, local minimizers and stable transition layers

Hurtado, Elard Juárez; Sônego, Maicon

doi:10.1016/j.jmaa.2019.123634

Cited by 3 publications

(2 citation statements)

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“…In several space dimensions, this definition of degeneracy (or criticality) should depend as well on the dimension d of the physical space (see [10,28] for further information). For a study of variational properties of subcritical (according to our definition) potentials with respect to the p−Laplacian, the reader is referred to [7] (see also the recent work [21]).…”

Section: Introductionmentioning

confidence: 99%

Long time dynamics of solutions to $p$-Laplacian diffusion problems with bistable reaction terms

Folino,

Plaza,

Strani

2020

Preprint

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This paper establishes the emergence of slowly moving transition layer solutions for the p-Laplacian (nonlinear) evolution equation,where ε > 0 and p ≥ 2 are constants, driven by the action of a family of double-well potentials of the formindexed by n ∈ N with minima at two pure phases u = ±1. The equation is endowed with initial conditions and boundary conditions of Neumann type. It is shown that interface layers, or solutions which initially are equal to ±1 except at a finite number of thin transitions of width ε, persist for an exponentially long time in the critical case with 2n = p, and for an algebraically long time in the supercritical (or degenerate) case with 2n > p. For that purpose, energy bounds for a renormalized effective energy potential of Ginzburg-Landau type are established. In contrast, in the subcritical case with 2n < p, the transition layer solutions are stationary.

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Section: Introductionmentioning

confidence: 99%

Long time dynamics of solutions to $p$-Laplacian diffusion problems with bistable reaction terms

Folino,

Plaza,

Strani

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…In several space dimensions, this definition of degeneracy (or criticality) should depend as well on the dimension d of the physical space (see [13,32] for further information). For a study of variational properties of subcritical (according to our definition) potentials with respect to the p−Laplacian, the reader is referred to [8] (see also the recent work [24]).…”

mentioning

confidence: 99%

Long time dynamics of solutions to $ p $-Laplacian diffusion problems with bistable reaction terms

Folino¹,

Plaza²,

Strani³

2021

DCDS

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A note on interface formation in singularly perturbed elliptic problems

Sônego

2020

Complex Variables and Elliptic Equations

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On the energy functionals derived from a non-homogeneous p-Laplacian equation: Γ-convergence, local minimizers and stable transition layers

Cited by 3 publications

References 29 publications

Long time dynamics of solutions to $p$-Laplacian diffusion problems with bistable reaction terms

Long time dynamics of solutions to $p$-Laplacian diffusion problems with bistable reaction terms

Long time dynamics of solutions to $ p $-Laplacian diffusion problems with bistable reaction terms

A note on interface formation in singularly perturbed elliptic problems

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