Existence and rigidity of the vectorial Peierls–Nabarro model for dislocations in high dimensions

DOI10.1088/1361-6544/ac24e3zbMath1478.35199arXiv2006.08107OpenAlexW4213209271MaRDI QIDQ5160609

Jian-Guo Liu, Zibu Liu, Yuan Gao

Publication date: 29 October 2021

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.08107

zbMATH Keywords

spectral analysisfractional LaplacianPeierls-Nabarro modelDe Giorgi conjecturestable entire solutionanisotropic nonlocal operatorenergy rearrangement

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Linear elasticity with initial stresses (74B10) Maximum principles in context of PDEs (35B50) Variational methods for elliptic systems (35J50) Boundary value problems for PDEs with pseudodifferential operators (35S15) PDEs in connection with mechanics of deformable solids (35Q74) Ginzburg-Landau equations (35Q56) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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New classifications of monotonicity investigation for discrete operators with Mittag-Leffler kernel ⋮ Asymptotic Stability for Diffusion with Dynamic Boundary Reaction from Ginzburg–Landau Energy ⋮ Existence and uniqueness of solutions to the Peierls–Nabarro model in anisotropic media ⋮ Uniform decay estimates for the semi-linear wave equation with locally distributed mixed-type damping via arbitrary local viscoelastic versus frictional dissipative effects ⋮ \(N\)-lump solutions to a \((3+1)\)-dimensional variable-coefficient generalized nonlinear wave equation in a liquid with gas bubbles

Cites Work

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• Local and global minimizers for a variational energy involving a fractional norm
• Ten equivalent definitions of the fractional Laplace operator
• On De Giorgi's conjecture in dimension \(N\geq 9\)
• Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result
• On a conjecture of De Giorgi and some related problems
• Phase transition with the line-tension effect
• A nonlocal anisotropic model for phase transitions
• Rigidity of minimizers in nonlocal phase transitions
• Asymptotics for the fractional Allen-Cahn equation and stationary nonlocal minimal surfaces
• Revisit of the Peierls-Nabarro model for edge dislocations in Hilbert space
• Long time behavior of dynamic solution to Peierls-Nabarro dislocation model
• On stable solutions for boundary reactions: a De Giorgi-type result in dimension \(4 + 1\)
• Existence and uniqueness of bounded stable solutions to the Peierls-Nabarro model for curved dislocations
• On the Motion of Curved Dislocations in Three Dimensions: Simplified Linearized Elasticity
• A De Giorgi–Type Conjecture for Minimal Solutions to a Nonlinear Stokes Equation
• Stochastic Peierls--Nabarro Model for Dislocations in High Entropy Alloys
• Rigidity of Minimizers in Nonlocal Phase Transitions II
• Dynamics for Systems of Screw Dislocations
• $\Gamma$-Limit of a Phase-Field Model of Dislocations
• An Extension Problem Related to the Fractional Laplacian
• Internal waves of permanent form in fluids of great depth
• Layer solutions in a half‐space for boundary reactions