TY - JOUR
T1 - Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem
JF - Atti Accad. Naz Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 17 (2006) 279-290
Y1 - 2006
A1 - Fethi Mahmoudi
A1 - Andrea Malchiodi
AB - 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 $k = 1$.
UR - http://hdl.handle.net/1963/2170
U1 - 2074
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -