Nonexistence of multi-bubble solutions to some elliptic equations on convex domains

By M. Grossi, Futoshi Takahashi. 2010

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Abstract We prove the nonexistence of multi-bubble solutions for several types of problems on smooth bounded convex domains. Problems we study include the Liouville equation − Δ u = λ e u in Ω , u = 0 on ∂ Ω in R 2 , where λ > 0 is a parameter, and the almost critical problem − Δ u = u N + 2 N − 2 − e , u > 0 in Ω , u = 0 on ∂ Ω in higher dimensions, where e > 0 .

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a2dfffd94b46ea525e6c0ff623a0b1331c42d758