Asymptotics for solutions of elliptic equations in double divergence form

2006/02/24 by Maz'ya, Vladimir, McOwen, Robert
#35J15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0602558

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 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.

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