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Quantization for an elliptic equation of order 2m with critical
, 2010
"... exponential nonlinearity ..."
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Critical points of the MoserTrudinger functional on a disk
, 2012
"... On the unit disk B1 ⊂ R2 we study the MoserTrudinger functional E(u) = e u2 − 1 dx, u ∈ H 1 0 (B1) and its restrictions EMΛ, where MΛ: = {u ∈ H 1 0 (B1) : ‖u ‖ 2 H 1 0 B1 = Λ} for Λ> 0. We prove that if a sequence uk of positive critical points of EMΛ (for some Λk> 0) blows up as k k → ∞, ..."
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On the unit disk B1 ⊂ R2 we study the MoserTrudinger functional E(u) = e u2 − 1 dx, u ∈ H 1 0 (B1) and its restrictions EMΛ, where MΛ: = {u ∈ H 1 0 (B1) : ‖u ‖ 2 H 1 0 B1 = Λ} for Λ> 0. We prove that if a sequence uk of positive critical points of EMΛ (for some Λk> 0) blows up as k k → ∞, then Λk → 4π, and uk → 0 weakly in H1 0 (B1) and strongly in C1 loc (B1 \ {0}). Using this we also prove that when Λ is large enough, then EMΛ has no positive critical point, complementing previous existence results by CarlesonChang, M. Struwe and LammRobertStruwe.