Two Slope Functions Minimizing Fractional Seminorms and Applications to Misfit Dislocations

DOI10.1137/23m1568910arXiv2207.04741OpenAlexW4391389381MaRDI QIDQ6202909

Emanuele Nunzio Spadaro, Lucia De Luca, Marcello Ponsiglione

Publication date: 27 February 2024

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.04741

zbMATH Keywords

periodic minimizersmisfit dislocationsfractional seminorms

Mathematics Subject Classification ID

Analysis of microstructure in solids (74N15) Crystals in solids (74N05) Fractional partial differential equations (35R11)

Cites Work

• Unnamed Item
• Striped periodic minimizers of a two-dimensional model for martensitic phase transitions
• Periodic minimizers in 1D local mean field theory
• Singular perturbations as a selection criterion for periodic minimizing sequences
• On energy minimizers of the diblock copolymer problem
• On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces
• Revisit of the Peierls-Nabarro model for edge dislocations in Hilbert space
• Uniform distribution of dislocations in Peierls-Nabarro models for semi-coherent interfaces
• The core-radius approach to supercritical fractional perimeters, curvatures and geometric flows
• The variational approach to \(s\)-fractional heat flows and the limit cases \(s \rightarrow 0^+\) and \(s \rightarrow 1^-\)
• A 1D Macroscopic Phase Field Model for Dislocations and a Second Order $\Gamma$-Limit
• The 0-fractional perimeter between fractional perimeters and Riesz potentials
• Dislocation Models of Crystal Grain Boundaries
• On the Stresses and Energies associated with Inter-Crystalline Boundaries

This page was built for publication: Two Slope Functions Minimizing Fractional Seminorms and Applications to Misfit Dislocations