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On the effect of domain geometry in singular perturbation problems. (English) Zbl 0970.35034

Singularly perturbed elliptic problems are considered. The single-peaked solutions are studied. It is shown that the location of maximum points of single-peaked solutions depends on the geometric properties of the domain. There are examples of domains for which the single-peaked set is calculated.

MSC:

35J60 Nonlinear elliptic equations
35B25 Singular perturbations in context of PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35B45 A priori estimates in context of PDEs
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