On a conjecture of De Giorgi about the phase-field approximation of the Willmore functional

DOI10.1007/s00205-023-01870-zOpenAlexW4365512793WikidataQ123298284 ScholiaQ123298284MaRDI QIDQ2698465

Giovanni Bellettini, Nicola Picenni, Mattia Freguglia

Publication date: 24 April 2023

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.04649

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for optimal control problems involving partial differential equations (49J20) Parabolic equations and parabolic systems (35Kxx) Elliptic equations and elliptic systems (35Jxx)

Cites Work

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• Phase-field approximations of the Willmore functional and flow
• A singular perturbation problem with integral curvature bound
• Applied functional analysis. Functional analysis, Sobolev spaces and elliptic differential equations
• Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
• The gradient theory of phase transitions and the minimal interface criterion
• On the approximation of the elastica functional in radial symmetry
• On a modified conjecture of De Giorgi
• Γ-type estimates for the one-dimensional Allen–Cahn’s action
• A new diffuse-interface approximation of the Willmore flow
• A Higher Order Asymptotic Problem Related to Phase Transitions
• Ordinary Differential Equations

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