Abstract:

The space of functions of bounded mean oscillation (BMO) was discovered by Fritz John in his consideration of problems in Elasticity. The study of this space and its properties has had a far reaching impact on harmonic analysis and its applications - as the dual of the Hardy space H¹, in Moser's proof of the regularity result of De Giorgi and Nash, as an endpoint in interpolation, a space on which translation invariant singular integrals (e.g. Riesz transforms) are bounded, and as a target in Sobolev embeddings that just miss .  However, its use in Elasticity has not been explored in great detail. In this talk I will discuss some recent work with S. Spector on applications of BMO in elasticity in which we obtain uniqueness results. This talk will cover material from several joint works, two completed and one in preparation.