Trace Operator’s Range Characterization for Sobolev Spaces on Lipschitz Domains of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>ℝ</mml:mi> <mml:mn>2</mml:mn> </mml:msup></mml:math>
نویسندگان
چکیده
We give, first, two new applications related to the range characterization of trace operator in H 2 (Ω). After this, we characterize Sobolev spaces W 3,p (Ω) when Ω is a connected bounded domain ℝ with Lipschitz-continuous boundary.
منابع مشابه
Trace Theorems for Sobolev Spaces on Lipschitz Domains. Necessary Conditions
A famous theorem of E. Gagliardo gives the characterization of traces for Sobolev spaces W 1, p (Ω) for 1 ≤ p < ∞ when Ω ⊂ R is a Lipschitz domain. The extension of this result to W m, p (Ω) for m ≥ 2 and 1 < p < ∞ is now well-known when Ω is a smooth domain. The situation is more complicated for polygonal and polyhedral domains since the characterization is given only in terms of local compati...
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ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2023
ISSN: ['1631-073X', '1778-3569']
DOI: https://doi.org/10.5802/crmath.407