%0 Journal Article %J Atti Accad. Naz Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 17 (2006) 279-290 %D 2006 %T Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem %A Fethi Mahmoudi %A Andrea Malchiodi %X We consider the equation $- \\\\e^2 \\\\D u + u = u^p$ in $\\\\O \\\\subseteq \\\\R^N$, where $\\\\O$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\pa \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, \\\\dots, N-2\\\\}$. We impose Neumann boundary conditions, assuming $1<\\\\frac{N-k+2}{N-k-2}$ and $\\\\e \\\\to 0^+$. This result settles in full generality a phenomenon previously considered only in the particular case $N = 3$ and $k = 1$. %B Atti Accad. Naz Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 17 (2006) 279-290 %G en_US %U http://hdl.handle.net/1963/2170 %1 2074 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-03T12:23:19Z\\nNo. of bitstreams: 1\\nMahmoudiMalchiodi06.pdf: 624613 bytes, checksum: 030160de63323a3b0c3864b8f5102b0b (MD5)