Geometry of quasiminimal phase transitions

DOI10.1007/S00526-007-0146-1zbMATH Open1156.35018OpenAlexW2048686291WikidataQ115387670 ScholiaQ115387670MaRDI QIDQ948952

Enrico Valdinoci, Alberto Farina

Publication date: 16 October 2008

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-007-0146-1

zbMATH Keywords

energy functionalHarnack-type inequalityCaffarelli-Cordoba-type inequalityquasiminimal perimeterzero mean curvaturee

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) A priori estimates in context of PDEs (35B45) Variational methods for second-order elliptic equations (35J20)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Translation of J. D. van der Waals' ``The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density
• Singular perturbations of variational problems arising from a two-phase transition model
• The geometry of mesoscopic phase transition interfaces
• The effect of a singular perturbation on nonconvex variational problems
• On a conjecture of De Giorgi and some related problems
• A negative answer to a one-dimensional symmetry problem in the Heisenberg group
• Geometric properties of Bernoulli-type minimizers
• Symmetry for solutions of semilinear elliptic equations in \(\mathbb{R}^N\) and related conjectures
• The gradient theory of phase transitions and the minimal interface criterion
• Mean curvature properties for \(p\)-Laplace phase transitions
• Regularity of flat level sets in phase transitions
• THE GINZBURG–LANDAU EQUATION IN THE HEISENBERG GROUP
• Nonconvex variational problems with anisotropic perturbations
• A gradient bound for entire solutions of quasi‐linear equations and its consequences
• Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
• Plane-like minimizers in periodic media: jet flows and Ginzburg-Landau-type functionals
• Uniform convergence of a singular perturbation problem
• Density Estimates for a Degenerate/Singular Phase-Transition Model
• Flat level set regularity of 𝑝-Laplace phase transitions
• Nonconvex Variational Problems With General Singular Perturbations
• On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property

Related Items (17)

The geometric theory of phase transitions ⋮ 1D symmetry for semilinear PDEs from the limit interface of the solution ⋮ Minimal configurations for the Frenkel-Kontorova model on a quasicrystal ⋮ Density Estimates for Degenerate Double-Well Potentials ⋮ Gradient Lagrangian systems and semilinear PDE ⋮ Density estimates for a variational model driven by the Gagliardo norm ⋮ Effects of geometry on transfer matrices, spin chains and critical behaviour ⋮ THE GINZBURG–LANDAU EQUATION IN THE HEISENBERG GROUP ⋮ Long-range Phase Coexistence Models: Recent Progress on the Fractional Allen-Cahn Equation ⋮ Phase transitions in geometrothermodynamics ⋮ Front propagation in geometric and phase field models of stratified media ⋮ Density estimates for a fluid jet model in the Heisenberg group ⋮ $1$D symmetry for solutions of semilinear and quasilinear elliptic equations ⋮ Unnamed Item ⋮ Multibump solutions and asymptotic expansions for mesoscopic Allen-Cahn type equations ⋮ Phase Transitions and Minimal Hypersurfaces in Hyperbolic Space ⋮ Density estimates for vector minimizers and applications

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