Relaxation of bulk and interfacial energies
From MaRDI portal
Publication:1817419
DOI10.1007/BF02198453zbMath0876.49037OpenAlexW2080304081MaRDI QIDQ1817419
Ana Cristina Barroso, Giusseppe Buttazzo, Irene Fonseca, Guy Bouchitté
Publication date: 27 October 1997
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02198453
Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45)
Related Items
VARIATIONAL APPROXIMATION OF FREE-DISCONTINUITY ENERGIES WITH LINEAR GROWTH ⋮ A global method for deterministic and stochastic homogenisation in \textit{BV} ⋮ Relaxation of variational problems under trace constraints ⋮ Relaxation in \(BV\) versus quasiconvexification in \(W^{1,p}\); a model for the interaction between fracture and damage ⋮ Second-order structured deformations: relaxation, integral representation and applications ⋮ Optimal flux densities for linear mappings and the multiscale geometry of structured deformations ⋮ Upscaling and spatial localization of non-local energies with applications to crystal plasticity ⋮ Relaxation for an optimal design problem inBD(Ω) ⋮ Dimension reduction in the context of structured deformations ⋮ \Gamma-convergence for free-discontinuity problems in linear elasticity: homogenization and relaxation ⋮ Unnamed Item ⋮ on a certain compactification of an arbitrary subset of ℝm and its applications to DiPerna-Majda measures theory
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Relaxation of quasiconvex functionals in \(BV(\Omega, \mathbb{R}^ N)\) for integrands \(f(x, u, \bigtriangledown u)\)
- Relaxation for a class of nonconvex functionals defined on measures
- Minimal interface criterion for phase transitions in mixtures of Cahn- Hilliard fluids
- Functionals with linear growth defined on vector valued BV functions
- Functionals defined on partitions in sets of finite perimeter. I: Integral representation and Gamma-convergence
- Functionals defined on partitions in sets of finite perimeter. II: Semicontinuity, relaxation and homogenization
- Integral representation of nonconvex functionals defined on measures
- On the relaxation in \(BV(\Omega ;\mathbb{R}^ m)\) of quasi-convex integrals
- An introduction to \(\Gamma\)-convergence
- A boundary-value problem for nematic liquid crystals with a variable degree of orientation
- Existence theorem for a minimum problem with free discontinuity set
- \(\Gamma\)-convergence, minimizing movements and generalized mean curvature evolution
- Relaxation in \(BV\) versus quasiconvexification in \(W^{1,p}\); a model for the interaction between fracture and damage
- Further remarks on the lower semicontinuity of polyconvex integrals
- Quasi-convexity and the lower semicontinuity of multiple integrals
- Optimal approximations by piecewise smooth functions and associated variational problems
- New lower semicontinuity results for nonconvex functionals defined on measures
- Weakly Differentiable Functions
- Quasi-Convex Integrands and Lower Semicontinuity in $L^1 $
- Relaxation of multiple integrals in the spaceBV(Ω, RP)
- Rank one property for derivatives of functions with bounded variation
- Anisotropic singular perturbations—the vectorial case
- The interaction between bulk energy and surface energy in multiple integrals
- On the lower semicontinuity of quasiconvex integrals in SBV(Ω, Rk)
- Relaxation results for some free discontinuity problems.
- Direct methods in the calculus of variations
This page was built for publication: Relaxation of bulk and interfacial energies
