A generalized Young measure comes from A-free measures exactly when it satisfies Jensen-type inequalities for all A-quasiconvex integrands and its concentration part lies in the wave cone.
$\mathrm{L}^1$-estimates for constant rank operators
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We show that the inequality $$ \|D^{k-1}(u-\pi u)\|_{\mathrm{L}^{n/(n-1)}(\mathbb{R}^n)}\leq c\|\mathbb{B}(D) u\|_{\mathrm{L}^1(\mathbb{R}^n)} $$ holds for vector fields $u\in\mathrm{C}^\infty_c$ if and only if $\mathbb{B}$ is canceling. Here $\pi$ denotes the $\mathrm{L}^2$-orthogonal projection onto the kernel of the $k$-homogeneous differential operator $\mathbb{B}(D)$ of \emph{constant rank} on $\mathbb{R}^n$. Other critical embeddings are established.
fields
math.AP 1years
2019 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
Characterization of generalized Young measures generated by $\mathcal A$-free measures
A generalized Young measure comes from A-free measures exactly when it satisfies Jensen-type inequalities for all A-quasiconvex integrands and its concentration part lies in the wave cone.