Compact embeddings of vector valued Sobolev and Besov spaces

By Herbert Amann. 2000

267 citations recorded by the source corpus.

The main result of this paper is a generalization and sharpening of the Aubin-Dubinskii lemma concerning compact subsets in vectorvalued Lebesque spaces. In addition, there are given some new embedding results for vector valued Besov spaces.

View Paper: https://www.semanticscholar.org/paper/f661987145ef850d4b75b3cc4904e7a1fdc6a946

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Citations in the corpus

Anisotropic function spaces and maximal regularity for parabolic problems Part 1: Function spaces (2009, background): “Schmeißer [53] under various restrictions on s and p.”
Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity (2018, unknown): “Again by means of a corresponding embedding property ([2]), an application thereof to appropriately large p > 1 shows that there exists θ1 ∈ (0, 1) such that for each τ > 0 we can pick C3 > 0 fulfilling ‖cε‖C1+θ1,θ1 (Ω̄×[t,t+2]) ≤ C3 for all t ≥ τ 2 .”
Sharp embedding results for spaces of smooth functions with power weights (2011, background): “Also vector-valued function spaces are intensively studied (see [2, 3, 36, 37, 38, 43, 45] and references therein).”
Maximal regularity with temporal weights for parabolic problems with inhomogeneous boundary conditions (2012, background): “We refer to [2], [19] or [24] for a definition and the properties of these spaces.”
How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? (2015, methodology): “8 by application of a standard embedding result ([2]).”
Long-term behaviour in a chemotaxis-fluid system with logistic source (2016, background): “For any q ∈ [1, 6) and any η > 0 there is T > 0 such that for any t > T one can find ε0 > 0 such that for any ε ∈ (0, ε0) ∫ t+1”
Local energy estimates and global solvability in a three-dimensional chemotaxis-fluid system with prescribed signal on the boundary (2021, methodology): “29) Now using that due to a well-known embedding result [43] the validity of (2.”
A topological and geometric approach to fixed points results for sum of operators and applications (2004, background): “Indeed if the above holds, L(I, E) is compacted embedded into W (I, F ) (see [1]).”
Linear parabolic problems involving measures (2001, unknown): “It is the latter case that has been considered in [5].”
A Note on Aubin-Lions-Dubinskiĭ Lemmas (2013, background): “[2] H. Amann.”
Degenerate parabolic stochastic partial differential equations (2013, unknown): “Furthermore, by the embeddings L p(TN ) ↩→ H−1(TN ), p ∈ [2,∞), and L2(TN ) ↩→ L p(TN ), p ∈ [1, 2), we conclude that, for all p ∈ [1,∞), ũ ∈ L p(Ω̃ × [0, T ], P̃, dP ⊗ dt; L p(TN )), where P̃ denotes the predictable σ -algebra associated to (F̃t )t≥0.”