Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4611442 | Journal of Differential Equations | 2012 | 23 Pages |
Abstract
Let Ω be a simply connected, open and bounded domain in R2. We are concerned with the nonlinear elliptic problem(0.1){âÎv=8Ïevâ«Î©evâ4Ïâj=1mαjδpjin Ω,v=0on âΩ, where αj>0, δpj denotes the Dirac mass with singular point pj and {p1,â¦,pm}âΩ. We provide necessary and sufficient conditions for the existence of solutions to (0.1). Our result is the two dimensional version of the sharp existence/nonexistence result obtained in Druet (2002) [13] for elliptic equations with critical exponent in dimension 3. In particular, we prove that the set Ω+m(α̲) is open, where, for a given α̲=(α1,â¦,αm)â(0,+â)Ãâ¯Ã(0,+â), Ω+m(α̲)={(p1,â¦,pm)| problem (0.1) has a solution}âΩÃâ¯ÃΩ.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
D. Bartolucci, C.S. Lin,