TY - JOUR T1 - Concentration of solutions for a singularly perturbed mixed problem in non-smooth domains JF - Journal of Differential Equations Y1 - 2013 A1 - Serena Dipierro KW - Finite-dimensional reductions KW - Local inversion KW - Singularly perturbed elliptic problems AB -

We consider a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ whose boundary has an $(n−2)$-dimensional singularity. Assuming $1<p<\frac{n+2}{n−2}$, we prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero.

VL - 254 UR - http://www.sciencedirect.com/science/article/pii/S0022039612003312 ER -