Abstract
For second-order elliptic systems with the natural energy space W2 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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Literature cited
J. Serrin, “Local behaviour of quasilinear elliptic equations,” Acta Math.,111, 247–302 (1964).
A. I. Koshelev, The Regularity of Solutions of Elliptic Equations and Systems [in Russian], Nauka, Moscow (1986).
V. A. Kondrat'ev and E. M. Landis, “Second-order semilinear equations with nonnegative characteristic form,” Mat. Zametki,44, No. 4, 457–468 (1988).
H. Brezis and L. Veron, “Removable singularities for some nonlinear elliptic equations,” Arch. Ration. Mech. Anal.,75, No. 1, 1–6 (1980).
L. Veron, “Singular solutions of some nonlinear elliptic equations,” Nonlinear Analysis,5, No. 3, 225–242 (1981).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1349–1358, October, 1992.
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Kalita, E.A. Order of isolated singularities of solutions of elliptic systems. Ukr Math J 44, 1235–1245 (1992). https://doi.org/10.1007/BF01057680
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DOI: https://doi.org/10.1007/BF01057680