On the convergence of critical points of the Ambrosio-Tortorelli functional

Variational problems in a geometric measure-theoretic setting (49Q20) Nonlinear elliptic equations (35J60) Methods involving semicontinuity and convergence; relaxation (49J45) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38)

Cites Work

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Local minimization, variational evolution and \(\Gamma\)-convergence
Critical points via \(\Gamma \)-convergence: general theory and applications
A second order minimality condition for the Mumford-Shah functional
Convergence results for critical points of the one-dimensional Ambrosio-Tortorelli functional with fidelity term
Harmonic and quasi-harmonic spheres
Gradient estimates and blow-up analysis for stationary harmonic maps
Harmonic and quasi-harmonic spheres. III: Rectifiability of the parabolic defect measure and generalized varifold flows
The Allen-Cahn equation on closed manifolds
Min-max for phase transitions and the existence of embedded minimal hypersurfaces
The Gibbs-Thompson relation within the gradient theory of phase transitions
Energy quantization for harmonic maps
Harmonic and quasi-harmonic spheres. II.
Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory.
Revisiting brittle fracture as an energy minimization problem
Existence and limiting behavior of min-max solutions of the Ginzburg-Landau equations on compact manifolds
Torus-like solutions for the Landau-de Gennes model. I: The Lyuksyutov regime
The second inner variation of energy and the Morse index of limit interfaces
Asymptotic behavior of Allen-Cahn-type energies and Neumann eigenvalues via inner variations
On the second inner variations of Allen-Cahn type energies and applications to local minimizers
Stable regular critical points of the Mumford-Shah functional are local minimizers
Numerical implementation of the variational formulation for quasi-static brittle fracture
Partial regularity for stationary harmonic maps at a free boundary
Minimal submanifolds from the abelian Higgs model
A quantization property for static Ginzburg-Landau vortices.
An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs
Optimal approximations by piecewise smooth functions and associated variational problems
Approximation of functional depending on jumps by elliptic functional via t-convergence
Probabilistic Solution of Ill-Posed Problems in Computational Vision
On the convergence of stable phase transitions
Spectrum and index of two-sided Allen–Cahn minimal hypersurfaces
Phase field model with a variable chemical potential
On the second inner variation of the Allen-Cahn functional and its applications
Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case
The Variational Approach to Fracture
Asymptotics for the Ginzburg-Landau equation in arbitrary dimensions

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