Lifting Properties of Sobolev Spaces

Viktor I. Burenkov ()
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Viktor I. Burenkov: Cardiff University, School of Mathematics

A chapter in Function Spaces, Differential Operators and Nonlinear Analysis, 2003, pp 231-236 from Springer

Abstract: Abstract We prove that a Sobolev-type inequality for an arbitrary open set ΩC R Nis equivalent to inequalities of such type with different exponents for Ω x I, where I is an interval, or Ω x Ω.The proofs are based on the factorisation property of the appropriate heat kernels. AMS subject classifications: 35P15, 35J25, 47A75, 47B25

Keywords: Sobolev inequalities; Neumann Laplacian; heat kernels (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-8035-0_12

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DOI: 10.1007/978-3-0348-8035-0_12

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