Density estimates for vector minimizers and applications

DOI10.3934/dcds.2015.35.5631zbMath1352.35055arXiv1403.7608OpenAlexW2963793241MaRDI QIDQ255551

Nicholas D. Alikakos, Giorgio Fusco

Publication date: 9 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.7608

zbMATH Keywords

polar form\(p\)-Laplacianstructure of minimizersisolated singularitiesAllen-Cahn functionalvector minimizers

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Degenerate elliptic equations (35J70) Variational methods for elliptic systems (35J50) Methods involving semicontinuity and convergence; relaxation (49J45) Variational methods for second-order elliptic equations (35J20) Second-order elliptic systems (35J47)

Related Items (9)

Layered solutions to the vector Allen-Cahn equation in \(\mathbb{R}^2\). Minimizers and heteroclinic connections ⋮ Density Estimates for Degenerate Double-Well Potentials ⋮ Unnamed Item ⋮ Entire minimizers of Allen-Cahn systems with sub-quadratic potentials ⋮ On the triple junction problem without symmetry hypotheses ⋮ Unnamed Item ⋮ On the growth of the energy of entire solutions to the vector Allen-Cahn equation ⋮ Connecting orbits in Hilbert spaces and applications to P.D.E ⋮ A comparison principle for vector-valued minimzers of semilinear elliptic energy, with application to dead cores

Cites Work

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• De Giorgi type results for elliptic systems
• Density estimates for a variational model driven by the Gagliardo norm
• Density estimates for phase transitions with a trace
• A maximum principle for systems with variational structure and an application to standing waves
• Entire solutions to equivariant elliptic systems with variational structure
• Minimal interface criterion for phase transitions in mixtures of Cahn- Hilliard fluids
• Geometry of quasiminimal phase transitions
• Vector-valued local minimizers of nonconvex variational problems
• The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces
• On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation
• Stationary layered solutions in \(\mathbb{R}^ 2\) for an Allen-Cahn system with multiple well potential
• Slow motion in the gradient theory of phase transitions via energy and spectrum
• Two results on entire solutions of Ginzburg-Landau system in higher dimensions
• Front propagation in geometric and phase field models of stratified media
• Regularity of flat level sets in phase transitions
• On some elementary properties of vector minimizers of the Allen-Cahn energy
• Equivariant entire solutions to the elliptic system \(\Delta u = W_u(u)\) for general \(G\)-invariant potentials
• A uniform estimate for positive solutions of semilinear elliptic equations
• Some basic facts on the system $\Delta u - W_{u} (u) = 0$
• Density Estimates for a Nonlocal Variational Model via the Sobolev Inequality
• Fast Reaction, Slow Diffusion, and Curve Shortening
• Reaction-Diffusion Processes and Evolution to Harmonic Maps
• Symmetric quadruple phase transitions
• On the connection problem for potentials with several global minima
• Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries
• Plane-like minimizers in periodic media: jet flows and Ginzburg-Landau-type functionals
• Uniform convergence of a singular perturbation problem
• A three-layered minimizer in R2 for a variational problem with a symmetric three-well potential
• A New Proof for the Existence of an Equivariant Entire Solution Connecting the Minima of the Potential for the System Δu − W_u(u) = 0
• On the structure of phase transition maps for three or more coexisting phases
• Ginzburg-Landau vortices

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