On the necessity of the constant rank condition for $L^p$ estimates

Andr\'e Guerra; Bogdan Rai\c{t}\u{a}

On the necessity of the constant rank condition for $L^p$ estimates

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arxiv 2007.00484 v1 pith:AZDR4AW7 submitted 2020-07-01 math.CA math.AP

André Guerra , Bogdan Raiţă This is my paper · ORCID

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keywords constantestimaterankconditionnecessityapplclassicalconsider

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abstract

We consider a generalization of the elliptic $L^p$-estimate suited for linear operators with non-trivial kernels. A classical result of Schulenberger and Wilcox (Ann. Mat. Pura Appl. (4) 88: 229-305, 1971) shows that if the operator has constant rank then the estimate holds. We prove necessity of the constant rank condition for such an estimate.

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Characterization of generalized Young measures generated by $\mathcal A$-free measures
math.AP 2019-08 accept novelty 8.0 of 10

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.

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