Geodesic
Removability of an isolated singularity for anisotropic elliptic equations with absorption
Sbornik. Mathematics, Tome 199 (2008) no. 7, pp. 1033-1050 
I. I. Skrypnik. Removability of an isolated singularity for anisotropic elliptic equations with absorption. Sbornik. Mathematics, Tome 199 (2008) no. 7, pp. 1033-1050. http://geodesic.mathdoc.fr/item/SM_2008_199_7_a4/
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     title = {Removability of an isolated singularity for anisotropic elliptic equations with absorption},
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is concerned with the investigation of solutions with a point singularity of the general elliptic equation $$ -\sum_{i=1}^n\frac\partial{\partial x_i} \biggl(\biggl|\frac{\partial u}{\partial x_i}\biggr|^{p_i-2}\frac{\partial u}{\partial x_i}\biggr)+|u|^{q-1}u=0. $$ A method for deriving new pointwise estimates for the solution and integral estimates for the gradient of the solution is developed. Precise conditions are established on the behaviour of the term characterizing the absorption to ensure the non-existence of solutions with a point singularity. Bibliography: 11 titles.

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