Sobolev-Type Inequalities on Manifolds in the Presence of Symmetries and Applications

Athanase Cotsiolis () and Nikos Labropoulos ()
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Athanase Cotsiolis: University of Patras, Department of Mathematics
Nikos Labropoulos: University of Patras, Department of Mathematics

A chapter in Contributions in Mathematics and Engineering, 2016, pp 45-68 from Springer

Abstract: Abstract In this article, we present some Sobolev-type inequalities on compact Riemannian manifolds with boundary, the data and the functions being invariant under the action of a compact subgroup of the isometry group. We investigate the best constants for the Sobolev, trace Sobolev, Nash, and trace Nash inequalities. By developing particular geometric properties of the manifold as well as of the solid torus, we can calculate the precise values of the best constants in the presented Sobolev-type inequalities. We apply these results to solve nonlinear elliptic, type Dirichlet and Neumann, PDEs of upper critical Sobolev exponent.

Keywords: Sobolev Inequality; Isometry Group; Tubular Neighborhood; Compact Riemannian Manifold; Good Constant (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-31317-7_3

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DOI: 10.1007/978-3-319-31317-7_3

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