Farkas, C., Kristály, A. & Mester, Á. (2021) Calculus of Variations and Partial Differential Equations [Matematică, Q1]

Publicat: 24 Iulie 2021

Farkas, C., Kristály, A. & Mester, Á. (2021) Compact Sobolev embeddings on non-compact manifolds via orbit expansions of isometry groups. Calculus of Variations and Partial Differential Equations, 60, 128.

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

✓ Publisher: Springer
✓ Web of Science Categories: Mathematics; Mathematics, Applied
✓ Web of Science Article Influence Score (AIS): 1.699 (2021) / Q1

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

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