Let be a bounded domain in with smooth boundary . We consider the equation , under zero Neumann boundary conditions, where is open, smooth and bounded and is a small positive parameter. We assume that there is a -dimensional closed, embedded minimal submanifold of , which is non-degenerate, and certain weighted average of sectional curvatures of is positive along . Then we prove the existence of a sequence and a positive solution such that
in the sense of measures, where stands for the Dirac measure supported on and is a positive constant.
Cite this article
Manuel del Pino, Fethi Mahmoudi, Monica Musso, Bubbling on boundary submanifolds for the Lin–Ni–Takagi problem at higher critical exponents. J. Eur. Math. Soc. 16 (2014), no. 8, pp. 1687–1748DOI 10.4171/JEMS/473