University of Sydney
Mon 27 October 2014 2-3pm, Carslaw 829 (AGR)
For and , we consider the nonlinear elliptic equation in , where denotes a domain in () containing . We obtain a complete classification of the behaviour near (as well as at if ) for all positive distribution solutions, together with corresponding existence results. When , any positive solution with a removable singularity at must be constant. The origin is a removable singularity for all positive solutions if and only if for any small (possible for ), where denotes any ball centred at with small radius and denotes the fundamental solution of the Laplacian. If for small , then any given positive solution has either removable singularity at , or or , where and are precisely determined positive constants. When , any positive solution is radially symmetric and non-increasing with (possibly any) non-negative limit at .
Check also the PDE Seminar page. Enquiries to Daniel Hauer or Daniel Daners.