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Sobolev spaces with variable exponents on Riemannian manifolds

Institution:	1. Department of Mathematics, Seattle University Seattle, WA, 98122, USA;2. Department of Mathematical Sciences, Saginaw Valley State University, University Center, MI, 48710, USA;1. Department of Mechanical Systems Engineering, Hiroshima Institute of Technology, 2-1-1 Miyake Saeki-ku Hiroshima 731-5193, Japan;2. Faculty of Education and Welfare Science, Oita University, Dannoharu Oita-city 870-1192, Japan;1. Department of Mathematics and Mathematical Statistics, Umeå University, SE-90187 Umeå, Sweden;2. Department of Mathematics, Uppsala University, SE-75106 Uppsala, Sweden;3. Department of Mathematics, KTH Royal Institute of Technology, SE-10044 Stockholm, Sweden;1. School of Mathematical Sciences, Nankai University, Tianjin 300071, PR China;2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, PR China;1. University of Jyväskylä, Department of Mathematics and Statistics, Mattilanniemi, 40100 Jyväskylä, Finland;2. Università di Padova, Dipartimento di Matematica “T. Levi-Civita”, via Trieste 63, 35121 Padova, Italy

Abstract:	In this article we study variable exponent Sobolev spaces on Riemannian manifolds. The spaces are examined in the case of compact manifolds. Continuous and compact embeddings are discussed. The paper contains an example of the application of the theory to elliptic equations on compact manifolds.

Keywords:	Lebesgue spaces with variable exponents Sobolev spaces Riemannian manifolds
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