(s, p)-Harmonic Approximation of Functions of Least Ws,1-Seminorm

Claudia Bucur; Serena Dipierro; Luca Lombardini; José M. Mazón; Enrico Valdinoci

doi:10.1093/imrn/rnab284

(s, p)-Harmonic Approximation of Functions of Least W^s,1-Seminorm

Claudia Bucur
, Serena Dipierro
, Luca Lombardini
, José M. Mazón
, Enrico Valdinoci

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We investigate the convergence as p ↘ 1 of the minimizers of the W^s,p-energy for s ∈ (0, 1) and p ∈ (1, ∞) to those of the W^s,1-energy, both in the pointwise sense and by means of Γ-convergence. We also address the convergence of the corresponding Euler-Lagrange equations and the equivalence between minimizers and weak solutions. As ancillary results, we study some regularity issues regarding minimizers of the W^s,1-energy.

Original language	English
Pages (from-to)	1173-1235
Number of pages	63
Journal	International Mathematics Research Notices
Volume	2023
Issue number	2
DOIs	https://doi.org/10.1093/imrn/rnab284
Publication status	Published - 1 Jan 2023

Funding

Funders	Funder number
ARC Australian Research Council	DE180100957

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10.1093/imrn/rnab284

Cite this

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abstract = "We investigate the convergence as p ↘ 1 of the minimizers of the Ws,p-energy for s ∈ (0, 1) and p ∈ (1, ∞) to those of the Ws,1-energy, both in the pointwise sense and by means of Γ-convergence. We also address the convergence of the corresponding Euler-Lagrange equations and the equivalence between minimizers and weak solutions. As ancillary results, we study some regularity issues regarding minimizers of the Ws,1-energy.",

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AU - Bucur, Claudia

AU - Dipierro, Serena

AU - Lombardini, Luca

AU - Mazón, José M.

AU - Valdinoci, Enrico

PY - 2023/1/1

Y1 - 2023/1/1

N2 - We investigate the convergence as p ↘ 1 of the minimizers of the Ws,p-energy for s ∈ (0, 1) and p ∈ (1, ∞) to those of the Ws,1-energy, both in the pointwise sense and by means of Γ-convergence. We also address the convergence of the corresponding Euler-Lagrange equations and the equivalence between minimizers and weak solutions. As ancillary results, we study some regularity issues regarding minimizers of the Ws,1-energy.

AB - We investigate the convergence as p ↘ 1 of the minimizers of the Ws,p-energy for s ∈ (0, 1) and p ∈ (1, ∞) to those of the Ws,1-energy, both in the pointwise sense and by means of Γ-convergence. We also address the convergence of the corresponding Euler-Lagrange equations and the equivalence between minimizers and weak solutions. As ancillary results, we study some regularity issues regarding minimizers of the Ws,1-energy.

UR - https://www.scopus.com/pages/publications/85152204493

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DO - 10.1093/imrn/rnab284

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ER -

(s, p)-Harmonic Approximation of Functions of Least W^s,1-Seminorm

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Partial Differential Equations, free boundaries and applications

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(s, p)-Harmonic Approximation of Functions of Least Ws,1-Seminorm

Abstract

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Partial Differential Equations, free boundaries and applications

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(s, p)-Harmonic Approximation of Functions of Least W^s,1-Seminorm