We investigate some asymptotic properties of extrema uα to the two-dimensional variational problem sup u∈H01(B) u∥=1 ∫B (eγu2 - 1)|x|α dx as α → +∞. Here B is the unit disk of ℝ2 and 0 < γ ≤ 4π is a given parameter. We prove that in a certain range of γ's, the maximizers are not radial for α large.
Serra, E., Secchi, S. (2006). Symmetry breaking results for problems with exponential growth in the unit disk. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 8(6), 823-839 [10.1142/S0219199706002295].
Symmetry breaking results for problems with exponential growth in the unit disk
SECCHI, SIMONE
2006
Abstract
We investigate some asymptotic properties of extrema uα to the two-dimensional variational problem sup u∈H01(B) u∥=1 ∫B (eγu2 - 1)|x|α dx as α → +∞. Here B is the unit disk of ℝ2 and 0 < γ ≤ 4π is a given parameter. We prove that in a certain range of γ's, the maximizers are not radial for α large.
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