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Sobolev space

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In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of L-norms of the function together with its ...

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索伯列夫空間 (Sobolev space)

简介

數學上,一個索伯列夫空間是一個由函數組成的賦範向量空間,對於某個給定的p ≥ 1,它對一個函數f和它的直到某個k階導數加上有限Lᵖ範數的這個條件。它以前蘇聯數學家謝爾蓋·索伯列夫來命名。 维基百科
Sobolev spaces are Banach spaces of smooth functions of one and several variables with conditions imposed on a few first (distributional) partial derivatives.
Let us briefly motivate our study of distributions and Sobolev spaces. ... Definition 1.2 The space of test functions in Ω, denoted D(Ω), is the.
4.1 The Sobolev space H1. 4.1.1 Convolution. We recall the definition of locally integrable functions on an open subset Ω of Rn,. L1,loc(Ω) := {f : Ω → K; ...
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作者:EW Weisstein2004 — This space is a Hilbert space for the inner product. <f,g>_(s,Omega)=sum_(|alpha. (3). Sobolev spaces play an important role in the theory of partial ...
Hence, we need the trace theorem. (Theorem 5.1) in order to be able to assign ”boundary values” along ∂Ω to a function in the. Sobolev space.
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作者:J KINNUNEN被引用次数:10 — Sobolev spaces. In this chapter we begin our study of Sobolev spaces. The Sobolev space is a vector space of functions that have weak derivatives.
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作者:T Dlotko被引用次数:6 — Generalized (Sobolev, weak) derivatives. Their properties, comparison with distributional deriva- tives. • Basic properties of Lp spaces and the space L1 loc.
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作者:E Brué2020被引用次数:13 — In this first section we prove the sharp Sobolev embedding inequality for the space Xy,p (see Theorem 1.5), an approximation result in ...

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