We consider a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions in a bounded domain Ω⊂Rn whose boundary has an (n- 2)-dimensional singularity. Assuming, 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.
Concentration of solutions for a singularly perturbed mixed problem in non-smooth domains / S. Dipierro. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 254:1(2013), pp. 30-66.
Concentration of solutions for a singularly perturbed mixed problem in non-smooth domains
S. Dipierro
2013
Abstract
We consider a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions in a bounded domain Ω⊂Rn whose boundary has an (n- 2)-dimensional singularity. Assuming, 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.
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