Let Ω be a simply connected, open and bounded domain in R2. We are concerned with the nonlinear elliptic problem (0.1) View the MathML source where αj>0, δpj denotes the Dirac mass with singular point pj and {p1,…,pm}⊂Ω. 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 View the MathML source is open, where, for a given View the MathML source, View the MathML source.
Bartolucci, D., Lin, C. (2012). Sharp existence results for mean field equations with singular data. JOURNAL OF DIFFERENTIAL EQUATIONS, 252, 4115-4137 [doi:10.1016/j.jde.2011.12.014].
Sharp existence results for mean field equations with singular data
BARTOLUCCI, DANIELE;
2012-01-01
Abstract
Let Ω be a simply connected, open and bounded domain in R2. We are concerned with the nonlinear elliptic problem (0.1) View the MathML source where αj>0, δpj denotes the Dirac mass with singular point pj and {p1,…,pm}⊂Ω. 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 View the MathML source is open, where, for a given View the MathML source, View the MathML source.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
