72 research outputs found
A variational approach of Sturm-Liouville problems with the nonlinearity depending on the derivative
Get PDFThree solutions for a class of quasilinear elliptic systems involving the p(x)-Laplace operator
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Nonlinear elliptic problems on Riemannian manifolds and applications to Emden–Fowler type equations
No full textA Sharp Sobolev Interpolation Inequality on Finsler Manifolds
No full textIn 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
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