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arXiv · 1702.06718

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

C. O. Alves·M. T. O. Pimenta
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Abstract

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.

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C. O. Alves, M. T. O. Pimenta. 2017-02-22. On existence and concentration of solutions to a class of quasilinear problems involving the $1-$Laplace operator. https://arxiv.org/abs/1702.06718

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