О порядке изолированных особенностей решений эллиптических систем

E. A. Kalita

E. A. Kalita Ин-т прикл. математики и механики АН Украины, Донецк

Abstract

For second–order elliptic systems with the natural energy space $W_2^1$solutions with an isolated singularity are considered. If the speed of growth of the solution is less than the limiting speed determined by the modulus of the elliptic system, it is proved that either the singularity is removable or its order coincides with the order of the singularity of the fundamental solution of Laplace's equation. Systems are also considered with positive nonlinear lowest terms, for which a complete classification is obtained of the possible orders of isolated singularities.

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On the order of isolated singularities of solutions to elliptic systems

Abstract

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