Elliptic problems on the ball endowed with Funk-type metrics

2014/08/06 by Kristály, Alexandru, Rudas, Imre J. · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1408.1300

Abstract

We study Sobolev spaces on the n-dimensional unit ball Bⁿ(1) endowed with a parameter-depending Finsler metric F_a, a∈ [0,1], which interpolates between the Klein metric (a=0) and Funk metric (a=1), respectively. We show that the standard Sobolev space defined on the Finsler manifold (Bⁿ(1),F_a) is a vector space if and only if a∈ [0,1). Furthermore, by exploiting variational arguments, we provide non-existence and existence results for sublinear elliptic problems on (Bⁿ(1),F_a) involving the Finsler-Laplace operator whenever a∈ [0,1).

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