On the non-locality of quasiconvexity
From MaRDI portal
Publication:1284041
DOI10.1016/S0294-1449(99)80006-7zbMath0932.49015OpenAlexW2035307337MaRDI QIDQ1284041
Publication date: 16 February 2000
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=AIHPC_1999__16_1_1_0
Existence theories for free problems in two or more independent variables (49J10) Methods involving semicontinuity and convergence; relaxation (49J45)
Related Items (35)
Equivalence between rank-one convexity and polyconvexity for isotropic sets of \({\mathbb R}^{2{\times}2}\). I ⋮ Equivalence between rank-one convexity and polyconvexity for isotropic sets of \({\mathbb R}^{2{\times}2}\). II ⋮ Legendre-Hadamard conditions for two-phase configurations ⋮ Numerical evidence towards a positive answer to Morrey's problem ⋮ When rank-one convexity meets polyconvexity: an algebraic approach to elastic binodal ⋮ Quasiconvexity and partial regularity via nonlinear potentials ⋮ Modelling of microstructure and its evolution in shape-memory-alloy single-crystals, in particular in CuAlNi ⋮ Approximation in multiscale modelling of microstructure evolution in shape-memory alloys ⋮ Adaptive algorithms for scalar non-convex variational problems ⋮ Marginal material stability ⋮ Weak Lower Semicontinuity of Integral Functionals and Applications ⋮ Beyond the classical Cauchy-Born rule ⋮ BMO \(\varepsilon\)-regularity results for solutions to Legendre-Hadamard elliptic systems ⋮ A method for pointwise evaluation of polyconvex envelopes ⋮ Singular multiple integrals and nonlinear potentials ⋮ Quasiconvex functions can be approximated by quasiconvex polynomials ⋮ Tartar's conjecture and localization of the quasiconvex hull in \(\mathbb R^{2\times 2}\) ⋮ Regularity of minima: an invitation to the dark side of the calculus of variations. ⋮ Singularities of minima: a walk on the wild side of the calculus of variations ⋮ A characterisation of the boundary displacements which induce cavitation in an elastic body ⋮ An algorithm for pointwise evaluation of polyconvex envelopes. II: generalization and numerical results ⋮ On various semiconvex relaxations of the squared-distance function ⋮ Ten remarks on nonconvex minimisation for phase transition simulations ⋮ On the lower semicontinuous quasiconvex envelope for unbounded integrands (I) ⋮ Atomistic to Continuum limits for computational materials science ⋮ Symmetric div-quasiconvexity and the relaxation of static problems ⋮ Harmonic type approximation lemmas ⋮ An estimate concerning the difference between minimizer and boundary value in some polyconvex problems ⋮ Jensen's inequality for the lower semicontinuous quasiconvex envelope and relaxation of multidimensional control problems ⋮ Relaxation of three solenoidal wells and characterization of extremal three-phase \(H\)-measures ⋮ New convexity conditions in the calculus of variations and compensated compactness theory ⋮ \(\mathscr{A}\)-quasiconvexity and partial regularity ⋮ Sets of lower semicontinuity and stability of integral functionals ⋮ Existence of minimisers of variational problems posed in spaces of mixed smoothness ⋮ Convergence of adaptive finite element methods for a nonconvex double-well minimization problem
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Formes quadratiques et calcul des variations
- Sets of gradients with no rank-one connections
- Null Lagrangians, weak continuity, and variational problems of arbitrary order
- Characterizations of Young measures generated by gradients
- An example of a quasiconvex function that is not polyconvex in two dimensions
- Convexity conditions and existence theorems in nonlinear elasticity
- Die Darstellung biquadratischer Formen als Summen von Quadraten mit Anwendung auf die Variationsrechnung
- Quasi-convexity and the lower semicontinuity of multiple integrals
- Laminates and microstructure
- Examples of rank-one convex functions
- Quasiconvex functions with subquadratic growth
- Rank-one convexity does not imply quasiconvexity
- On the planar rank-one convexity condition
- Quasi-Convexity and Lower Semi-Continuity of Multiple Variational Integrals of Any Order
- Direct methods in the calculus of variations
This page was built for publication: On the non-locality of quasiconvexity
