Locating the peaks of least-energy solutions to a quasilinear elliptic Neumann problem

Details Locating the peaks of least-energy solutions to a quasilinear elliptic Neumann problem Locating the peaks of least-energy solutions to a quasilinear elliptic Neumann problem

2007-04-03

arxiv.org/abs/0704.0402v1

Mathematics

Analysis of PDEs

Keywords: Quasilinear Neumann problem, m-Laplacian operator, least-energy solution, exponential decay, mean curvature.

Scientific paper

10.1093/imamat/hxl032

In this paper we study the shape of least-energy solutions to a singularly perturbed quasilinear problem with homogeneous Neumann boundary condition. We use an intrinsic variation method to show that at limit, the global maximum point of least-energy solutions goes to a point on the boundary faster than the linear rate and this point on the boundary approaches to a point where the mean curvature of the boundary achieves its maximum. We also give a complete proof of exponential decay of least-energy solutions.

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