On the complex constant rank condition and inequalities for differential operators

DOI10.1016/j.na.2023.113435arXiv2302.07528OpenAlexW4388314870MaRDI QIDQ6185365

Publication date: 8 January 2024

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2302.07528

zbMATH Keywords

differential operators Sobolev embedding Korn's inequality constant rank condition

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
On rank one convex functions that are homogeneous of degree one
Automatic convexity of rank-1 convex functions
A non-inequality for differential operators in the $L_ 1$ norm
Solutions of the divergence operator on John domains
Estimates for $L^{1}$-vector fields under higher-order differential conditions
New estimates for elliptic equations and Hodge type systems
A new approach to counterexamples to $L^1$ estimates: Korn's inequality, geometric rigidity, and regularity for gradients of separately convex functions
New estimates for the Laplacian, the div-curl, and related Hodge systems
Limiting Sobolev inequalities for vector fields and canceling linear differential operators
On Korn-Maxwell-Sobolev inequalities
An optimal Sobolev embedding for $L^1$
On the necessity of the constant rank condition for $L^p$ estimates
Limiting Bourgain-Brezis estimates for systems of linear differential equations: theme and variations
On the trace operator for functions of bounded $\mathbb{A} $-variation
Embeddings for $\mathbb{A}$-weakly differentiable functions on domains
Optimal embeddings into Lorentz spaces for some vector differential operators via Gagliardo's lemma
Coerciveness inequalities for nonelliptic systems of partial differential equations
Boundary estimates for elliptic systems with $L^{1}$- data
On the existence of certain singular integrals
Maxwell meets Korn: A new coercive inequality for tensor fields in RN×N with square-integrable exterior derivative
On Singular Integrals
A decomposition technique for John domains
Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension
Pointwise multiplicative inequalities and Nirenberg type estimates in weighted Sobolev spaces
$\cal A$-Quasiconvexity, Lower Semicontinuity, and Young Measures
Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates
On limiting trace inequalities for vectorial differential operators
Remarks On Ornstein’s Non-Inequality In ℝ2×2
Formulas to represent functions by their derivatives
Extension and representation of divergence-free vector fields on bounded domains
Optimal incompatible Korn-Maxwell-Sobolev inequalities in all dimensions

This page was built for publication: On the complex constant rank condition and inequalities for differential operators