Fine properties of functions of bounded deformation -- an approach via linear PDEs
From MaRDI portal
Publication:2128531
DOI10.3934/mine.2020018zbMath1487.35001arXiv1911.01356OpenAlexW3007909697MaRDI QIDQ2128531
Filip Rindler, Guido De Philippis
Publication date: 22 April 2022
Published in: Mathematics in Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1911.01356
Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Spaces of measures, convergence of measures (28A33) Absolutely continuous real functions of several variables, functions of bounded variation (26B30) Special properties of functions of several variables, Hölder conditions, etc. (26B35) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) PDEs with measure (35R06)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On rank one convex functions that are homogeneous of degree one
- On the structure of \({\mathcal A}\)-free measures and applications
- Integral representation for functionals defined on \(SBD^p\) in dimension two
- Characterization of generalized Young measures generated by symmetric gradients
- Automatic convexity of rank-1 convex functions
- Geometry of measures in \(R^ n:\) Distribution, rectifiability, and densities
- Relaxation of quasiconvex functionals in \(BV(\Omega, \mathbb{R}^ N)\) for integrands \(f(x, u, \bigtriangledown u)\)
- Lower semicontinuity for integral functionals in the space of functions of bounded deformation via rigidity and Young measures
- An integral formula for total gradient variation
- A non-inequality for differential operators in the \(L_ 1\) norm
- Characterization of generalized gradient Young measures generated by sequences in \(W^{1,1}\) and BV
- Fine phase mixtures as minimizers of energy
- Compactness and lower semicontinuity properties in \(SBD(\Omega)\)
- Functions of bounded deformation
- New integral estimates for deformations in terms of their nonlinear strains
- Characterizations of Young measures generated by gradients
- On the relaxation in \(BV(\Omega ;\mathbb{R}^ m)\) of quasi-convex integrals
- Gradient Young measures generated by sequences in Sobolev spaces
- Fine properties of functions with bounded deformation
- On lower semicontinuity of integral functionals in \(LD(\Omega)\)
- Variational methods for problems from plasticity theory and for generalized Newtonian fluids
- On the singular part of measures constrained by linear PDEs and applications
- On the two-state problem for general differential operators
- A new approach to counterexamples to \(L^1\) estimates: Korn's inequality, geometric rigidity, and regularity for gradients of separately convex functions
- Regularity of quasiconvex envelopes
- Dimensional estimates and rectifiability for measures satisfying linear PDE constraints
- Characterizations of symmetric polyconvexity
- Approximation of functions with small jump sets and existence of strong minimizers of Griffith's energy
- An elementary proof of the rank-one theorem for BV functions
- Optimal embeddings into Lorentz spaces for some vector differential operators via Gagliardo's lemma
- \({\mathcal {A}}\)-free rigidity and applications to the compressible Euler system
- On Saint Venant's compatibility conditions and Poincaré's lemma
- A local proof for the characterization of Young measures generated by sequences in BV
- A lower semicontinuity result for some integral functionals in the space \(SBD\)
- Su una teoria generale della misura \((r-1)\)-dimensionale in uno spazio ad \(r\) dimensioni
- Lower semicontinuity and Young measures in BV without Alberti's Rank-One Theorem
- Sets of Finite Perimeter and Geometric Variational Problems
- Traces of functions of bounded deformation
- Quasi-Convex Integrands and Lower Semicontinuity in $L^1 $
- Un espace fonctionnel pour les équations de la plasticité
- Rank one property for derivatives of functions with bounded variation
- A Piecewise Korn Inequality in SBD and Applications to Embedding and Density Results
- A Korn-type inequality in SBD for functions with small jump sets
- Which special functions of bounded deformation have bounded variation?
- $\cal A$-Quasiconvexity, Lower Semicontinuity, and Young Measures
- On a conjecture of Cheeger
- ON THE STRUCTURE OF MEASURES CONSTRAINED BY LINEAR PDES
- On the Integral Representation of Variational Functionals on $BD$
- Classical Fourier Analysis
- Calculus of variations
