Geodesic
Bubbling along boundary geodesics near the second critical exponent
Journal of the European Mathematical Society, Tome 12 (2010) no. 6, pp. 1553-1605 Cet article a éte moissonné depuis la source EMS Press

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The role of the second critical exponent p=(n+1)/(n−3), the Sobolev critical exponent in one dimension less, is investigated for the classical Lane–Emden–Fowler problem Δu+up=0, u>0 under zero Dirichlet boundary conditions, in a domain Ω in Rn with bounded, smooth boundary. Given Γ, a geodesic of the boundary with negative inner normal curvature we find that for p=(n+1)/(n−3)−ε, there exists a solution uε​ such that ∣∇uε​∣2 converges weakly to a Dirac measure on Γ as ε→0+ exists, provided that Γ is non-degenerate in the sense of second variations of length and ε remains away from certain explicit discrete set of values for which a resonance phenomenon takes place.
DOI : 10.4171/jems/241
Classification : 32-XX, 35-XX, 00-XX
Keywords: Critical Sobolev exponent, blowing-up solution, non degenerate geodesic 
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     author = {Manuel del Pino and Monica Musso and Frank Pacard},
     title = {Bubbling along boundary geodesics near the second critical exponent},
     journal = {Journal of the European Mathematical Society},
     pages = {1553--1605},
     year = {2010},
     volume = {12},
     number = {6},
     doi = {10.4171/jems/241},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/241/}
}
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Manuel del Pino; Monica Musso; Frank Pacard. Bubbling along boundary geodesics near the second critical exponent. Journal of the European Mathematical Society, Tome 12 (2010) no. 6, pp. 1553-1605. doi: 10.4171/jems/241

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