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)

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• Nonconvex variational problems with anisotropic perturbations
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• 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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