Minimax Critical Points in Ginzburg-Landau Problems with Semi-Stiff Boundary Conditions: Existence and Bubbling

DOI10.1080/03605302.2013.851214zbMath1296.35036OpenAlexW2137187949MaRDI QIDQ2875584

Volodymyr Rybalko, Petru Mironescu, Etienne Sandier, Leonid Berlyand

Publication date: 8 August 2014

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2013.851214

zbMATH Keywords

Ginzburg-Landaububblingmountain passprescribed degreesWente estimates

Mathematics Subject Classification ID

Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Variational methods for second-order elliptic equations (35J20)

Related Items (12)

Harmonic maps with prescribed degrees on the boundary of an annulus and bifurcation of catenoids ⋮ On the behavior of solutions of nonlinear Schrödinger equation with exponential growth ⋮ Renormalised energies and renormalisable singular harmonic maps into a compact manifold on planar domains ⋮ On energy-critical half-wave maps into \(\mathbb {S}^2\) ⋮ Renormalized energies for unit-valued harmonic maps in multiply connected domains ⋮ High frequency approximation of solutions to Klein–Gordon equation in Orlicz framework ⋮ On a fractional Ginzburg-Landau equation and 1/2-harmonic maps into spheres ⋮ Size of planar domains and existence of minimizers of the Ginzburg-Landau energy with semistiff boundary conditions ⋮ Profile decomposition and phase control for circle-valued maps in one dimension ⋮ Minimizing \(1/2\)-harmonic maps into spheres ⋮ Ginzburg-Landau relaxation for harmonic maps on planar domains into a general compact vacuum manifold ⋮ Distances between homotopy classes ofW^s,p(𝕊^N;𝕊^N)

Cites Work

• Unnamed Item
• Solutions with vortices of a semi-stiff boundary value problem for the Ginzburg-Landau equation
• A general wavelet-based profile decomposition in the critical embedding of function spaces
• A global compactness result for elliptic boundary value problems involving limiting nonlinearities
• Near boundary vortices in a magnetic Ginzburg-Landau model: their locations via tight energy bounds
• Ginzburg-Landau minimizers with prescribed degrees. capacity of the domain and emergence of vortices
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Convergence of solutions of H-systems or how to blow bubbles
• Homotopy classes in Sobolev spaces and the existence of energy minimizing maps
• The existence of minimal immersions of 2-spheres
• A boundary value problem related to the Ginzburg-Landau model
• Analysis of the lack of compactness in the critical Sobolev embeddings
• Lifting in Sobolev spaces
• Elliptic partial differential equations of second order
• On uniqueness of vector-valued minimizers of the Ginzburg-Landau functional in annular domains
• Degree theory of BMO. I: Compact manifolds without boundaries
• Uniqueness of vortexless Ginzburg-Landau type minimizers in two dimensions
• Dual variational methods in critical point theory and applications
• Degree theory and BMO. II: Compact manifolds with boundaries. (Appendix with Petru Mironescu)
• Local minimizers of the Ginzburg-Landau functional with prescribed degrees
• Nonexistence of Ginzburg-Landau minimizers with prescribed degree on the boundary of a doubly connected domain
• An existence theorem for surfaces of constant mean curvature
• MINIMIZERS OF THE MAGNETIC GINZBURG–LANDAU FUNCTIONAL IN SIMPLY CONNECTED DOMAIN WITH PRESCRIBED DEGREE ON THE BOUNDARY
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz
• Description of the lack of compactness for the Sobolev imbedding
• Stability in 2D Ginzburg-Landau passes to the limit

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