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arXiv:1702.06718 [math.AP]AbstractReferencesReviewsResources

On existence and concentration of solutions to a class of quasilinear problems involving the $1-$Laplace operator

C. O. Alves, M. T. O. Pimenta

Published 2017-02-22Version 1

In this work we use variational methods to prove results on existence and concentration of solutions to a problem in $\mathbb{R}^N$ involving the $1-$Laplacian operator. A thorough analysis on the energy functional defined in the space of functions of bounded variation $BV(\mathbb{R}^N)$ is necessary, where the lack of compactness is overcome by using the Concentration of Compactness Principle of Lions.

Categories: math.AP
Subjects: 35J62, 35J20
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