Constant rank operators: lower semi-continuity and L1-estimates

Thesis

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.

Authors: Raita, B

• DOI: 10.5287/ora-8rx8vaxwz
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford