72 research outputs found
A variational approach of Sturm-Liouville problems with the nonlinearity depending on the derivative
A Sharp Sobolev Interpolation Inequality on Finsler Manifolds
In this paper we study a sharp Sobolev interpolation inequality on Finsler
manifolds. We show that Minkowski spaces represent the optimal framework for the
Sobolev interpolation inequality on a large class of Finsler manifolds: (1) Minkowski
spaces support the sharp Sobolev interpolation inequality; (2) any complete Berwald
space with non-negative Ricci curvature which supports the sharp Sobolev interpolation
inequality is isometric to a Minkowski space. The proofs are based on properties
of the Finsler–Laplace operator and on the Finslerian Bishop–Gromov volume comparison
theorem
- …