Compact Sets in the Space L~(O,
By J. SIMeoN, Jacqves Snwo. 2005
1,879 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/6e0853e8b8abada12038c4d8aa257ea5e46558e9
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Citations in the corpus
- Pullback attractors in V for non-autonomous 2D-Navier-Stokes equations and their tempered behaviour (2012, unknown): “Then, using in particular the Aubin-Lions compactness lemma (see [1], [17] or [25]) there exists an element u ∈ L∞(t− 2, t;V )∩L(2)(t− 2, t;D(A)) with u′ ∈ L(2)(t − 2, t;H), such that for a subsequence (relabelled the same) the following convergences hold: u ∗ ⇀ u weak-star in L”
- Exact boundary controllability of the nonlinear Schrödinger equation (2009, background): “20) It follows from Aubin’s lemma (see [30]) and (3.”
- Well-posedness of stochastic partial differential equations with fully local monotone coefficients (2022, background): “The following lemma is the Theorem 5 of [82].”
- Pullback attractors for 2D-Navier-Stokes equations with delays in continuous and sub-linear operators (2009, background): “From the above estimates, the compactness of the injection of V in H, and the Aubin theorem (see [14] or [20] or [1]) we obtain that there exist a subsequence of u (that we relabel the same) and a function u ∈ L2p(−h, T ;H) ∩ L∞(0, T ;H) ∩ L(2)(0, T ;V ) for all T > 0, with u = φ in (−h, 0), and the”
- Regularity for a Schrödinger equation with singular potentials and application to bilinear optimal control (2005, background): “Simon, Theorem 5 in [9]), up to a subsequence we also have the strong convergence un → u in C([0, T ];H 1 loc).”
- Optimal location of controllers for the one-dimensional wave equation (2013, unknown): “[25]), it follows that, up to a subsequence, the sequence (φχωn )n∈IN converges weakly in L(2)(0, T ;L(2)(0, π)) ∩ H(1)(0, T ;H−1(0, π)) and strongly in L(2)(0, T ;L(2)(0, π)) to some φ̃.”