101. Concentration of solutions for a singularly perturbed mixed problem in non-smooth domains
- Author
-
Serena Dipierro
- Subjects
Singular perturbation ,Applied Mathematics ,Mathematical analysis ,Boundary (topology) ,Mixed boundary condition ,Mathematics::Spectral Theory ,Method of matched asymptotic expansions ,Domain (mathematical analysis) ,symbols.namesake ,Mathematics - Analysis of PDEs ,Singularly perturbed elliptic problems ,Dirichlet boundary condition ,FOS: Mathematics ,Neumann boundary condition ,symbols ,Boundary value problem ,Finite-dimensional reductions ,Analysis ,Local inversion ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
We consider a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions in a bounded domain Ω ⊂ R n whose boundary has an ( n − 2 ) -dimensional singularity. Assuming 1 p 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.
- Published
- 2013