On the lower semicontinuous quasiconvex envelope for unbounded integrands (I)
From MaRDI portal
Publication:3603211
DOI10.1051/cocv:2008067zbMath1173.26009OpenAlexW2138193418MaRDI QIDQ3603211
Publication date: 16 February 2009
Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/245348
representation theoremquasiconvex functionquasiconvex envelopeunbounded functionMorrey's integral inequality
Methods involving semicontinuity and convergence; relaxation (49J45) Convexity of real functions of several variables, generalizations (26B25) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Representation and superposition of functions (26B40)
Related Items
A relaxation result in the vectorial setting and power law approximation for supremal functionals ⋮ Homogenization of unbounded singular integrals in \(W^{1,\infty}\) ⋮ A note on locking materials and gradient polyconvexity ⋮ The quasiconvex envelope of conformally invariant planar energy functions in isotropic hyperelasticity ⋮ Homogenization of nonconvex integrals with convex growth ⋮ Quasiconvex relaxation of multidimensional control problems with integrandsf(t,ξ,v) ⋮ Jensen's inequality for the lower semicontinuous quasiconvex envelope and relaxation of multidimensional control problems
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Quasiconvexity and relaxation of nonconvex problems in the calculus of variations
- \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
- Piecewise continuous controls in Dieudonné-Rashevsky type problem
- Pontryagin's maximum principle for multidimensional control problems in image processing
- Characterizations of Young measures generated by gradients
- On the structure of quasiconvex hulls
- On the non-locality of quasiconvexity
- Implicit partial differential equations
- An algebraic characterization of quasi-convex functions
- Cauchy-Dirichlet problem for first order nonlinear systems
- General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases
- Bauer's maximum principle and hulls of sets
- On the relaxation and the Lavrentieff phenomenon for variational integrals with pointwise measurable gradient constraints
- The relaxation of some classes of variational integrals with pointwise continuous-type gradient constraints
- Elastic-plastic torsion problem. III
- Quasi-convexity and the lower semicontinuity of multiple integrals
- On the quasiconvex exposed points
- From Mumford–Shah to Perona–Malik in image processing
- Calculus of variations, implicit partial differential equations and microstructure
- Detection of Intensity and Motion Edges within Optical Flow via Multidimensional Control
- Finite extensions of convex functions
- Rank-one convexity does not imply quasiconvexity
- Two Convex Counterexamples: A Discontinuous Envelope Function and a Nondifferentiable Nearest-Point Mapping
- State Constraints in Convex Control Problems of Bolza
- Direct methods in the calculus of variations