Existence and uniqueness of bounded stable solutions to the Peierls-Nabarro model for curved dislocations
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Publication:2663596
DOI10.1007/s00526-021-01939-1zbMath1462.35437arXiv2003.12782OpenAlexW3141881697WikidataQ115386753 ScholiaQ115386753MaRDI QIDQ2663596
Publication date: 19 April 2021
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2003.12782
Nonlinear elliptic equations (35J60) Variational methods for elliptic systems (35J50) Fractional partial differential equations (35R11) Ginzburg-Landau equations (35Q56) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
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Cites Work
- Unnamed Item
- Unnamed Item
- Local and global minimizers for a variational energy involving a fractional norm
- Regularity results for stable-like operators
- Energy estimates and 1-D symmetry for nonlinear equations involving the half-Laplacian
- Rigidity of minimizers in nonlocal phase transitions
- Schauder estimates for a class of non-local elliptic equations
- 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 \(4 + 1\)
- Some energy estimates for stable solutions to fractional Allen-Cahn equations
- Quantitative flatness results and \(BV\)-estimates for stable nonlocal minimal surfaces
- Sharp energy estimates for nonlinear fractional diffusion equations
- Improvement of Flatness for Nonlocal Phase Transitions
- Nonlocal phase transitions: rigidity results and anisotropic geometry
- Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions
- Layer solutions in a half‐space for boundary reactions
