Geodesic
Bubbling on boundary submanifolds for the Lin–Ni–Takagi problem at higher critical exponents
Journal of the European Mathematical Society, Tome 16 (2014) no. 8, pp. 1687-1748

Voir la notice de l'article provenant de la source EMS Press

Let Ω be a bounded domain in Rn with smooth boundary ∂Ω. We consider the equation d2Δu−u+un−k−2n−k+2​=0 in Ω , under zero Neumann boundary conditions, where Ω is open, smooth and bounded and d is a small positive parameter. We assume that there is a k-dimensional closed, embedded minimal submanifold K of ∂Ω, which is non-degenerate, and certain weighted average of sectional curvatures of ∂Ω is positive along K. Then we prove the existence of a sequence d=dj​→0 and a positive solution ud​ such that
DOI : 10.4171/jems/473
Classification : 35-XX
Keywords: Critical Sobolev exponent, blowing-up solutions, nondegenerate minimal submanifolds 
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     author = {Manuel del Pino and Fethi Mahmoudi and Monica Musso},
     title = {Bubbling on boundary submanifolds for the {Lin{\textendash}Ni{\textendash}Takagi} problem at higher critical exponents},
     journal = {Journal of the European Mathematical Society},
     pages = {1687--1748},
     publisher = {mathdoc},
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Manuel del Pino; Fethi Mahmoudi; Monica Musso. Bubbling on boundary submanifolds for the Lin–Ni–Takagi problem at higher critical exponents. Journal of the European Mathematical Society, Tome 16 (2014) no. 8, pp. 1687-1748. doi: 10.4171/jems/473

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