Title: Continuity of a Right Inverse of the Divergence Operator
Abstract: The divergence of a vector field u = (u1, ... , un), often written as div u = L,j=1 or V · u, is·a well-known quantity in vector calculus, rneasuring 'sinks' and 'sources' Of u. In fluid dynamics, this quantity manifests itself in the compression and rarefaction of a fluid whose velocity is given by u. The incompressibility condition on _such a fluid, formulated as div u = 0, is well-known. A more general case, div u = J, is naturally a PDE of interest.
Given J E L§(D), a right inverse of divergence can be constructed from a singular integral kernel and used to solve div u = f. In my talk, I present a proof (due to Ricardo G.Duran) that this right inverse is bounded from L§ (fl) to HJ (l1r using the Fourier transform and elementary techniques.