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PDE Seminar Abstracts

Classification of isolated singularities for equations involving the Finsler-Laplace operator

Mihai Mihăilescu
University of Craiova, Romania
Wednesday 21 November 2012 11:15am, AGR Carslaw 829

Abstract

In this talk, we consider anisotropic elliptic operators such as

Lλ,Hu:=-(H(u)(H)(u))-λH(x)2u,in {xN:0<H(x)<1},

where H and H are polar Finsler norms on N (N3) and -<λ(N-2)24. When H(x)=|x|, where |x| denotes the euclidian norm on N, operator Lλ,Hu becomes the classical Hardy-Sobolev operator-Δu-λ|x|2u. We completely classify the behavior near the origin for all positive weak solutions of Lλ,Hu=0 in {xN:0<H(x)<1}. We establish that either uΦ+λγ+(0,) or uΦ-λγ-(0,), as |x|0, where Φ±λ denote the fundamental solutions of Lλ,Hu=0. This is a joint work with F. Cîrstea.