Isolated singularities of positive solutions of p-Laplacian type equations in R^d

Details Isolated singularities of positive solutions of p-Laplacian type equations in R^d Isolated singularities of positive solutions of p-Laplacian type equations in R^d

2010-08-23

arxiv.org/abs/1008.3873v2

Mathematics

Analysis of PDEs

25 pages, considerably improved version

Scientific paper

We study the behavior of positive solutions of p-Laplacian type elliptic equations of the form Q'(u) := -p-Laplacian(u) + V |u|^(p-2) u = 0 in Omega near an isolated singular point zeta, where 1 < p < inf, Omega is a domain in R^d with d > 1, and zeta = 0 or zeta = inf. We obtain removable singularity theorems for positive solutions near zeta. In particular, using a new three-spheres theorems for certain solutions of the above equation near zeta we prove that if V belongs to a certain Kato class near zeta and p>d (respectively, p

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