Characterisation of zero trace functions in higher-order spaces of Sobolev type
| Autor: | David E. Edmunds, Aleš Nekvinda |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Function space
Applied Mathematics 010102 general mathematics Mathematical analysis 01 natural sciences Sobolev inequality 010101 applied mathematics Combinatorics Sobolev space Bounded function Interpolation space Order (group theory) Standard probability space 0101 mathematics Analysis Sobolev spaces for planar domains Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 459:879-892 |
| ISSN: | 0022-247X |
| Popis: | Let Ω be a bounded open subset of R n with a mild regularity property, let m ∈ N and p ∈ ( 1 , ∞ ) , and let W m , p ( Ω ) be the usual Sobolev space of order m based on L p ( Ω ) ; the closure in W m , p ( Ω ) of the smooth functions with compact support is denoted by W 0 m , p ( Ω ) . A special case of the results given below is that u ∈ W 0 m , p ( Ω ) if and only if all distributional derivatives of u of order m belong to L p ( Ω ) and u / d m ∈ L 1 ( Ω ) , where d ( x ) = dist ( x , ∂ Ω ) . In fact what is proved is the analogous result when the Sobolev space is based on a member of a class of Banach function spaces that includes both L p ( Ω ) and L p ( ⋅ ) ( Ω ) , the Lebesgue space with variable exponent p ( ⋅ ) satisfying natural conditions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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