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
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Burenkov, V.I. (2003). Lifting Properties of Sobolev Spaces. In: Haroske, D., Runst, T., Schmeisser, HJ. (eds) Function Spaces, Differential Operators and Nonlinear Analysis. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8035-0_12
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DOI: https://doi.org/10.1007/978-3-0348-8035-0_12
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9414-2
Online ISBN: 978-3-0348-8035-0
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