Corrections to: Vector-valued local minimizers of nonconvex variational problems

DOI10.1216/RMJM/1181072968zbMath0760.49008OpenAlexW2083179746MaRDI QIDQ1206764

Peter Sternberg

Publication date: 1 April 1993

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181072968

zbMATH Keywords

singular perturbationsnonconvex variational problemsepi- convergencenon-constant vector-valued local minimizersperturbed variational problems

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for problems in abstract spaces (49J27) Variational methods for second-order elliptic equations (35J20)

Related Items (13)

A sharp-interface limit for a two-well problem in geometrically linear elasticity ⋮ Interfacial energy and the Maxwell rule ⋮ On the competition of elastic energy and surface energy in discrete numerical schemes ⋮ Existence of minimizers for non-quasiconvex integrals ⋮ Sharp-interface limit of a multi-phase spectral shape optimization problem for elastic structures ⋮ Local minimizers and planar interfaces in a phase-transition model with interfacial energy ⋮ A variant of the mountain pass theorem and variational gluing ⋮ Variational approximation of anisotropic functionals on partitions ⋮ Solutions of mountain pass type for double well potential systems ⋮ Local minimizer and de Giorgi's type conjecture for the isotropic-nematic interface problem ⋮ Two-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitions ⋮ Bound kink states in inhomogeneous nonlinear media ⋮ On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation

Cites Work

• The effect of a singular perturbation on nonconvex variational problems
• Asymptotic location of nodal lines using geodesic theory
• The gradient theory of phase transitions for systems with two potential wells
• Local minimisers and singular perturbations
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