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Locating the peaks of semilinear elliptic systems

Alessio Pomponio·Marco Squassina
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Abstract

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 $Σ$ 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 $Σ$ in the sense of subdifferential calculus.

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Alessio Pomponio, Marco Squassina. 2005-06-09. Locating the peaks of semilinear elliptic systems. https://arxiv.org/abs/math/0506139

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