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Title: Constant rank operators : lower semi-continuity and L1-estimates
Author: Raita, Bogdan
ISNI:       0000 0004 7653 5845
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2018
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In the first part of this work we investigate lower semi-continuity of integral functionals defined on vector fields that satisfy linear pde constraints that satisfy the so-called constant rank condition. In particular, we simplify the definition of A-quasiconvexity and characterize a class of A-free generalized Young measures by duality with A-quasiconvex functions. In the second part we investigate linear L1-estimates, i.e., study linear (overdetermined) elliptic systems with L1-data. We extend Van Schaftingen's inequalities to constant rank operators, give a new embedding into bounded functions at the endpoint of the theory, study pointwise properties and integrability of restrictions of solutions, and give a generalization of the Gagliardo-Nirenberg inequality on domains.
Supervisor: Kristensen, Jan ; Seregin, Gregory Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available