Asymptotics for solutions of elliptic equations in double divergence form
Analysis of PDEs
2007-05-23 v2
Abstract
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 \delta_{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.
Keywords
Cite
@article{arxiv.math/0602558,
title = {Asymptotics for solutions of elliptic equations in double divergence form},
author = {Vladimir Maz'ya and Robert McOwen},
journal= {arXiv preprint arXiv:math/0602558},
year = {2007}
}
Comments
14 pages. The Abstract and Introduction have been rewritten; this includes an additional Corollary of our main results