The Oseen-Frank energy functional on manifolds

DOI10.1007/s10013-020-00468-2zbMath1472.35142OpenAlexW3124290648MaRDI QIDQ2042266

Min-Chun Hong

Publication date: 28 July 2021

Published in: Vietnam Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10013-020-00468-2

zbMATH Keywords

partial regularityOseen-Frank energy

Mathematics Subject Classification ID

Variational methods for elliptic systems (35J50) Elliptic equations on manifolds, general theory (58J05)

Cites Work

• Global existence of solutions of the liquid crystal flow for the Oseen-Frank model in \(\mathbb R^2\)
• A new approximation of relaxed energies for harmonic maps and the Faddeev model
• Harmonic maps between surfaces (with a special chapter on conformal mappings)
• Existence of infinitely many equilibrium configurations of a liquid crystal system prescribing the same nonconstant boundary value
• A regularity theory for harmonic maps
• On the evolution of harmonic mappings of Riemannian surfaces
• Harmonic maps with defects
• Existence and partial regularity of static liquid crystal configurations
• Existence and partial regularity results for the heat flow for harmonic maps
• Stable defects of minimizers of constrained variational principles
• Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds
• The Dirichlet energy of mappings with values into the sphere
• The existence of minimal immersions of 2-spheres
• On the regularity of the minima of variational integrals
• Regularity of minimizers of relaxed problems for harmonic maps
• Well-posedness of the Ericksen-Leslie system with the Oseen-Frank energy in \(L_{\mathrm{uloc}}^{3}({\mathbb R}^3)\)
• Some constitutive equations for liquid crystals
• Blow-up Criteria of Strong Solutions to the Ericksen-Leslie System in ℝ³
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• A Report on Harmonic Maps
• Morse Theory by Perturbation Methods with Applications to Harmonic Maps
• Convergence of the Ginzburg-Landau Approximation for the Ericksen-Leslie System
• Partial regularity of weak solutions of the liquid crystal equilibrium system
• Harmonic Mappings of Riemannian Manifolds
• Riemannian geometry and geometric analysis
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item