Abstract
Let (M,g) be a smooth compact Riemannian manifold, and G a subgroup of the isometry group of (M,g). We compute the value of the best constant in Sobolev inequalities when the functions are G-invariant. Applications to non-linear PDEs of critical or upper critical Sobolev exponent are also presented.
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Faget, Z. Best Constants in Sobolev Inequalities on Riemannian Manifolds in the Presence of Symmetries. Potential Analysis 17, 105–124 (2002). https://doi.org/10.1023/A:1015776915614
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DOI: https://doi.org/10.1023/A:1015776915614