English

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

R2 v1 2026-07-22T17:31:59.518Z