On a Sharp Poincaré-Type Inequality on the 2-Sphere and its Application in Micromagnetics

DOI10.1137/19M1238757zbMath1420.35012arXiv1901.04334OpenAlexW2911023027MaRDI QIDQ5231345

Valeriy V. Slastikov, Arghir Zarnescu, Giovanni Di Fratta

Publication date: 26 August 2019

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

Full work available at URL: https://arxiv.org/abs/1901.04334

zbMATH Keywords

vector spherical harmonicsmagnetic skyrmionsspherical thin films

Mathematics Subject Classification ID

Partial differential inequalities and systems of partial differential inequalities (35R45) Statistical mechanics of magnetic materials (82D40) Variational principles of physics (49S05) Variational methods for eigenvalues of operators (49R05) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (9)

The mathematics of thin structures ⋮ A unified divergent approach to Hardy-Poincaré inequalities in classical and variable Sobolev spaces ⋮ Poincaré type inequality for hypersurfaces and rigidity results ⋮ Curved thin-film limits of chiral Dirichlet energies ⋮ On symmetry of energy minimizing harmonic-type maps on cylindrical surfaces ⋮ Variational Principles of Micromagnetics Revisited ⋮ A quantitative description of skyrmions in ultrathin ferromagnetic films and rigidity of degree \(\pm 1\) harmonic maps from \(\mathbb{R}^2\) to \(\mathbb{S}^2\) ⋮ Micromagnetics of curved thin films ⋮ Curvature-stabilized skyrmions with angular momentum

Cites Work

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• Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
• On the extremal functions of Sobolev-Poincaré inequality
• Spherical functions of mathematical geosciences. A scalar, vectorial, and tensorial setup
• Sobolev spaces on Riemannian manifolds
• Liouville type results for local minimizers of the micromagnetic energy
• Optimal \(L^p\)-Riemannian Gagliardo-Nirenberg inequalities
• Acoustic and electromagnetic equations. Integral representations for harmonic problems

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