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
Pomponio, A., Squassina, M., Locating the peaks of semilinear elliptic systems, <<ADVANCED NONLINEAR STUDIES>>, 2005; 5 (4): 441-460. [doi:10.1515/ans-2005-0401] [http://hdl.handle.net/10807/92795]
Locating the peaks of semilinear elliptic systems
Squassina, MarcoUltimo
2005
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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