Relaxation for Partially Coercive Integral Functionals with Linear Growth

DOI10.1137/18M1199460zbMath1450.49006arXiv1806.00343OpenAlexW3090287125MaRDI QIDQ5127142

Publication date: 21 October 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.00343

zbMATH Keywords

calculus of variations BV functions geometric measure theory weak monotonicity $\mathrm{L}^1$-relaxation

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Geometric measure and integration theory, integral and normal currents in optimization (49Q15)

Related Items (1)

Liftings, Young measures, and lower semicontinuity

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Relaxation of quasiconvex functionals in $BV(\Omega, \mathbb{R}^ N)$ for integrands $f(x, u, \bigtriangledown u)$
Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in $n$ variabili
Minimal interface criterion for phase transitions in mixtures of Cahn- Hilliard fluids
Characterization of generalized gradient Young measures generated by sequences in $W^{1,1}$ and BV
Existence and partial regularity results for the heat flow for harmonic maps
Integral representation on $BV(\Omega )$ of $\Gamma$-limits of variational integrals
Variational integrals on mappings of bounded variation and their lower semicontinuity
Minimal currents, geodesics, and relaxation of variational integrals on mappings of bounded variation
On the relaxation in $BV(\Omega ;\mathbb{R}^ m)$ of quasi-convex integrals
A global method for relaxation
Convex variational problems. Linear, nearly linear and anisotropic growth conditions
Liftings, Young measures, and lower semicontinuity
Phase transitions of elastic solid materials
The gradient theory of phase transitions and the minimal interface criterion
On lower semicontinuity and relaxation
Phase transition for potentials of high-dimensional wells
STRICTLY CONTINUOUS EXTENSION OF FUNCTIONALS WITH LINEAR GROWTH TO THE SPACE BV
Reaction-Diffusion Processes and Evolution to Harmonic Maps
The gradient theory of phase transitions for systems with two potential wells
The effective bulk energy of the relaxed energy of multiple integrals below the growth exponent
Quasi-Convex Integrands and Lower Semicontinuity in $L^1 $
Rank one property for derivatives of functions with bounded variation
Strict convergence and minimal liftings in BV
A Γ‐convergence result for the two‐gradient theory of phase transitions

This page was built for publication: Relaxation for Partially Coercive Integral Functionals with Linear Growth