Abstract for the talk at 13.11.2007 (16:45 h)

Michalis Kontovourkis (MPI MIS, Leipzig)

A regularity result for elliptic equations with low-regularity divergence-free coefficients

We study the equation for divergence-free vector fields with low regularity. Classical theory for general (not necessarily divergence-free) requires at least . It has been known for some time that for divergence-free coefficients, one can get results when . We show that for one can even go below the exponent n/2, and is sufficient.