SMS scnews item created by Daniel Daners at Tue 11 Sep 2012 0847
Type: Seminar
Modified: Tue 11 Sep 2012 0902; Tue 11 Sep 2012 0905
Distribution: World
Expiry: 17 Sep 2012
Calendar1: 17 Sep 2012 1400-1500
CalLoc1: AGR Carslaw 829
Auth: daners@bari.maths.usyd.edu.au

# Local behaviour of singular solutions for nonlinear elliptic equations in divergence form

### Cirstea

Florica Cîrstea
The University of Sydney
17 Sep 2012, 2-3pm, Carslaw Room 829 (AGR)

## Abstract

A complete classification of the behaviour near zero of all non-negative solutions of $$-\Delta u+u^q=0$$ in the punctured unit ball $$B_1(0)\setminus \{0\}$$ in $$R^N$$ ($$N\geq 3$$) is due to Veron (1981) for $$11$$. Here, $$A$$ denotes a positive $$C^1(0,1]$$ function which is regularly varying at zero with index in $$(2-N,2)$$. We show that zero is a removable singularity for all positive solutions if and only if $$\Phi\not\in L^q(B_1(0))$$, where $$\Phi$$ denotes the fundamental solution of $$-\nabla\cdot(A(|x|)\nabla u)=\delta_0$$ in the sense of distributions on $$B_1(0)$$, and $$\delta_0$$ is the Dirac mass at $$0$$. We also completely classify the isolated singularities in the more delicate case that $$\Phi\in L^q(B_1(0))$$. This is joint work with B. Brandolini, F. Chiacchio and C. Trombetti.

Check also the PDE Seminar page. Enquiries to Florica Cîrstea or Daniel Daners.

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