Compact Sobolev embeddings on non-compact manifolds via orbit expansions of isometry groups

نویسندگان

چکیده

Abstract Given a complete non-compact Riemannian manifold ( M , g ) with certain curvature restrictions, we introduce an expansion condition concerning group of isometries G that characterizes the coerciveness in sense Skrzypczak and Tintarev (Arch Math 101(3): 259–268, 2013). Furthermore, under these conditions, compact Sobolev-type embeddings à la Berestycki-Lions are proved for full range admissible parameters (Sobolev, Moser-Trudinger Morrey). We also consider case Randers-type Finsler manifolds finite reversibility constant inheriting similar embedding properties as their companions; sharpness such constructions shown by means Funk model. As application, quasilinear PDE on Randers spaces is studied using above variational arguments.

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ژورنال

عنوان ژورنال: Calculus of Variations and Partial Differential Equations

سال: 2021

ISSN: ['0944-2669', '1432-0835']

DOI: https://doi.org/10.1007/s00526-021-01997-5