Asymptotics for solutions of elliptic equations in double divergence form

Maz'ya, Vladimir; McOwen, Robert

Asymptotics for solutions of elliptic equations in double divergence form

Authors

Description

We consider weak solutions of the adjoint equation for an elliptic operator in nondivergent form, and their asymptotic properties at an interior point. We assume that the coefficients a_{ij} are bounded, measurable, complex-valued functions that approach δ_{ij}, but possibly at a slow rate. Our main result is an explicit formula for the leading asymptotic term for solutions with a most a mild singularity at x=0. As a consequence, we obtain upper and lower estimates for the L^p-norm of solutions, as well as necessary and sufficient conditions for solutions to be bounded or tend to zero in L^p-mean as r tends to zero.
14 pages. The Abstract and Introduction have been rewritten; this includes an additional Corollary of our main results