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.
Locating the peaks of semilinear elliptic systems / Pomponio, A; Squassina, M. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - 5:4(2005), pp. 441-460. [10.1515/ans-2005-0401]
Locating the peaks of semilinear elliptic systems
Pomponio, A;
2005-01-01
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 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.File in questo prodotto:
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