Locating the peaks of semilinear elliptic systems

Details Locating the peaks of semilinear elliptic systems Locating the peaks of semilinear elliptic systems

2005-06-08

arxiv.org/abs/math/0506139v2

Adv. Nonlinear Stud., 5, (2005), 441-460.

Mathematics

Analysis of PDEs

To appear on Advanced Nonlinear Studies, 21 pages

Scientific paper

We consider a system of weakly coupled singularly perturbed semilinear elliptic equations. First, we obtain a Lipschitz regularity result for the associated ground energy function $\Sigma$ as well as representation formulas for the left and the right derivatives. Then, we show that the concentration points of the solutions locate close to the critical points of $\Sigma$ in the sense of subdifferential calculus.

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