Sharp conditions for the classical asymptotic behaviour near a point for solutions to quasilinear elliptic systems

Article type: Research Article

Authors: Kozlov, Vladimir | Maz'ya, Vladimir

Affiliations: Mathematical Department, Linköpings Universitet, 581 83 Linköping, Sweden E‐mail: [email protected]

Note: [] The authors were supported by the Swedish Research Council (VR).

Abstract: It is well known that distributional solutions of an elliptic equation with constant coefficients behave asymptotically near an interior point as sums of polynomials and linear combinations of derivatives of a fundamental solution. We consider a class of quasilinear elliptic systems and give mild conditions ensuring the same asymptotic behaviour. The sharpness of our conditions is illustrated by examples. The results are obtained as corollaries of a general theorem on the asymptotics of solutions to nonlinear ordinary differential equations in Banach spaces.

Journal: Asymptotic Analysis, vol. 38, no. 2, pp. 143-165, 2004