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Asymptotics for solutions of elliptic equations in double divergence form

Vladimir Maz'ya·Robert McOwen
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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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Vladimir Maz'ya, Robert McOwen. 2006-03-24. Asymptotics for solutions of elliptic equations in double divergence form. https://arxiv.org/abs/math/0602558

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