Quasiconvexity, Null Lagrangians, and Hardy Space Integrability Under Constant Rank Constraints
André Guerra, Bogdan Raiţă
Abstract
Abstract We present a systematic treatment of the theory of Compensated Compactness under Murat’s constant rank assumption. We give a short proof of a sharp weak lower semicontinuity result for signed integrands, extending aspects of the results of Fonseca–Müller. The null Lagrangians are an important class of signed integrands, since they are the weakly continuous functions. We show that they are precisely the compensated compactness quantities with Hardy space integrability, thus proposing an answer to a question raised by Coifman–Lions–Meyer–Semmes. Finally we provide an effective way of computing the null Lagrangians associated with a given operator.
Topics & Concepts
Null (SQL)Constant (computer programming)Rank (graph theory)Space (punctuation)Hardy spaceMathematicsMathematical physicsMathematical analysisPure mathematicsPhysicsComputer scienceCombinatoricsOperating systemDatabaseProgramming languageAdvanced Harmonic Analysis ResearchNonlinear Partial Differential EquationsHolomorphic and Operator Theory