A non-inequality for differential operators in the \(L_ 1\) norm
From MaRDI portal
Publication:775630
DOI10.1007/BF00253928zbMath0106.29602MaRDI QIDQ775630
Publication date: 1962
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Related Items (99)
Lipschitz Spaces on Stratified Groups ⋮ On the singular part of measures constrained by linear PDEs and applications ⋮ Fine properties of functions of bounded deformation -- an approach via linear PDEs ⋮ Unnamed Item ⋮ Subcoercivity and subelliptic operators on Lie groups. I: Free nilpotent groups ⋮ On rank one convex functions that are homogeneous of degree one ⋮ On the equation 𝑑𝑖𝑣𝑌=𝑓 and application to control of phases ⋮ Best constants for two families of higher order critical Sobolev embeddings ⋮ Nonmultipliers of the Sobolev spaces \(W^{k,1}({\mathbb{R}}^ n)\) ⋮ Lp-trace-free generalized Korn inequalities for incompatible tensor fields in three space dimensions ⋮ Weakly coercive non-quasi-elliptic systems of differential operators in \(W _{l}^{p} (\mathbb R^{n})\) ⋮ Bilevel Training Schemes in Imaging for Total Variation--Type Functionals with Convex Integrands ⋮ Best constants in a borderline case of second-order Moser type inequalities ⋮ On approximate differentiability of functions with bounded deformation ⋮ Quasiconvexity, null Lagrangians, and Hardy space integrability under constant rank constraints ⋮ The divergence equation with \(L^{\infty}\) source ⋮ On the continuity of Fourier multipliers on \(\dot{W}^{l,1}(\mathbb{R}^d)\) and \(\dot{W}^{l,\infty}(\mathbb{R}^d)\) ⋮ The heat semigroup and integrability of Lie algebras: Lipschitz spaces and smoothness properties ⋮ On the continuity of Fourier multipliers on the homogeneous Sobolev spaces \(\dot{W}_1^1(R^d)\) ⋮ Fourier Multipliers of the Homogeneous Sobolev Space Ẇ 1,1 ⋮ Subelliptic operators on Lie groups: Variable coefficients ⋮ The heat semigroup and integrability of Lie algebras ⋮ The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces ⋮ Korn's inequality and John domains ⋮ A Piecewise Korn Inequality in SBD and Applications to Embedding and Density Results ⋮ Sharp conditions for Korn inequalities in Orlicz spaces ⋮ Korn type inequalities in Orlicz spaces ⋮ On Symmetric div-quasiconvex hulls and divsym-free \(\mathrm{L}^\infty\)-truncations ⋮ The regularity of minima for the Dirichlet problem on BD ⋮ Korn's inequality in anisotropic Sobolev spaces ⋮ On Korn's first inequality in a Hardy-Sobolev space ⋮ A Korn-type inequality in SBD for functions with small jump sets ⋮ Symmetric-convex functionals of linear growth ⋮ A fractional Korn-type inequality ⋮ Relaxation for an optimal design problem inBD(Ω) ⋮ Some functional properties on Cartan-Hadamard manifolds of very negative curvature ⋮ Calculus of variations. Abstracts from the workshop held August 14--20, 2022 ⋮ Study of viscoplastic flows governed by the Norton-Hoff operator ⋮ Optimal incompatible Korn-Maxwell-Sobolev inequalities in all dimensions ⋮ On the fractional Korn inequality in bounded domains: counterexamples to the case \(ps < 1\) ⋮ The equation divu + 〈a,u〉 = f ⋮ On the complex constant rank condition and inequalities for differential operators ⋮ Boundary ellipticity and limiting \(\mathrm{L}^1\)-estimates on halfspaces ⋮ On Sobolev classes containing solutions to Fokker-Planck-Kolmogorov equations ⋮ On the Integral Representation of Variational Functionals on $BD$ ⋮ Unnamed Item ⋮ Multipliers of Sobolev spaces ⋮ On the necessity of the constant rank condition for \(L^p\) estimates ⋮ On the \(L^p\)-differentiability of certain classes of functions ⋮ Partial regularity for symmetric quasiconvex functionals on BD ⋮ Some Poincaré-type inequalities for functions of bounded deformation involving the deviatoric part of the symmetric gradient ⋮ Sobolev regularity for convex functionals on BD ⋮ Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori ⋮ Continuity and canceling operators of order \(n\) on \(\mathbb{R}^n\) ⋮ On estimates for the tensor product of two homogeneous elliptic operators ⋮ Characterization of generalized Young measures generated by symmetric gradients ⋮ Poincaré meets Korn via Maxwell: extending Korn's first inequality to incompatible tensor fields ⋮ Automatic convexity of rank-1 convex functions ⋮ Limiting Bourgain-Brezis estimates for systems of linear differential equations: theme and variations ⋮ An extension of the notion of the order of a distribution ⋮ A pasting lemma and some applications for conservative systems ⋮ Local $\mathbf {L}^{1}$ estimates for elliptic systems of complex vector fields ⋮ A new approach to counterexamples to \(L^1\) estimates: Korn's inequality, geometric rigidity, and regularity for gradients of separately convex functions ⋮ Dislocation microstructures and the effective behavior of single crystals ⋮ Lower semicontinuity for integral functionals in the space of functions of bounded deformation via rigidity and Young measures ⋮ Generalized stress concentration factors for equilibrated forces and stresses ⋮ Inequalities for functions of the classes \(W^{\overrightarrow{m}}_p(R^n)\) ⋮ On critical \(\mathrm{L}^p\)-differentiability of BD-maps ⋮ On Korn-Maxwell-Sobolev inequalities ⋮ A survey about the equation \(\mathrm{div} u=f\) in bounded domains of \(\mathbb R^n\) ⋮ Variational Analysis of a Two-Dimensional Frustrated Spin System: Emergence and Rigidity of Chirality Transitions ⋮ On coercivity and irregularity for some nonlinear degenerate elliptic systems ⋮ Counterexamples to the \(L^p\)-Calderón-Zygmund estimate on open manifolds ⋮ Variable exponent Bochner-Lebesgue spaces with symmetric gradient structure ⋮ The \(L^p\)-Calderón-Zygmund inequality on non-compact manifolds of positive curvature ⋮ On an analogue of the de~Leeuw and Mirkil theorem for operators with variable coefficients ⋮ Comparison of Commuting One-Parameter Groups of Isometries ⋮ Homogeneous Fourier and Weyl multipliers on Sobolev spaces related to the Heisenberg group ⋮ Optimal limiting embeddings for \(\Delta\)-reduced Sobolev spaces in \(L^1\) ⋮ Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy ⋮ Lie groups and Lipschitz spaces ⋮ On the trace operator for functions of bounded \(\mathbb{A} \)-variation ⋮ \(L^1\)-Poincaré inequalities for differential forms on Euclidean spaces and Heisenberg groups ⋮ Sobolev inequalities for the symmetric gradient in arbitrary domains ⋮ Unnamed Item ⋮ L1 Sobolev estimates for (pseudo)-differential operators and applications ⋮ Some regularity theorems for operators in an enveloping algebra ⋮ Quasi-elliptic and weakly coercive systems in Sobolev spaces of vector functions ⋮ Some interpolation inequalities involving Stokes operator and first order derivatives ⋮ Critical 𝐿^{𝑝}-differentiability of 𝐵𝑉^{}𝔸-maps and canceling operators ⋮ Embeddings for \(\mathbb{A}\)-weakly differentiable functions on domains ⋮ Differential properties of functions and coerciveness in spaces with uniform norm ⋮ Korn's inequality and eigenproblems for the Lamé operator ⋮ A Bourgain-Brezis-Mironescu representation for functions with bounded deformation ⋮ Rank-one convex functions on \(2\times 2\) symmetric matrices and laminates on rank-three lines ⋮ On limiting trace inequalities for vectorial differential operators ⋮ Minimal number of significant directional moduli of smoothness ⋮ The Calderón-Zygmund inequality and Sobolev spaces on noncompact Riemannian manifolds ⋮ Trace-Free Korn Inequalities in Orlicz Spaces
This page was built for publication: A non-inequality for differential operators in the \(L_ 1\) norm