Optimal Lp-Lq-estimates for parabolic boundary value problems with inhomogeneous data
By Robert Denk, Matthias Hieber, Jan Prüss. 2007
340 citations recorded by the source corpus.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f9153aa098700aaf0317eac7b20bffe876729ca7
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Citations in the corpus
- Stable and unstable manifolds for quasilinear parabolic systems with fully nonlinear boundary conditions (2006, methodology): “Suppose that (R) is true and that (E) and (LS) hold for all u0 = u (t), t 2 J. Then we can apply Theorem 2.1 of [ 15 ] also to A (t) and B (t)), t 2 J, since the lower order terms A0(u (t))u (t) F0(u (t)) do not enter into (E) and (LS) of [15] and their coecients belong to L1(J ◊ ; B(E)) +Lp(J ◊ ; B”
- Anisotropic function spaces and maximal regularity for parabolic problems Part 1: Function spaces (2009, methodology): “Prüss [20], [21] established a maximal Lp-Lq-regularity theory for (P) for differential and boundary operators with operator-valued coefficients using recent Fourier multiplier theorems for operatorvalued symbols.”
- Time fractional diffusion equations: solution concepts, regularity, and long-time behavior (2019, methodology): “g the abstract theory from [51, Theorem 3.4, Theorem 3.6] to the time fractional diffusion equation (1) in the full space Rd and using results on the interpolation of Sobolev spaces (see e.g. [40] and [10]) we obtain the following result. Theorem 2.1. Let p,q ∈ (1,∞) and α ∈ (1 p,1). Then the problem”
- Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities (2015, background): “the apriori estimates in Lemmas 2.1–2.3, and 2.4, where Ω is replaced by Qε,still hold for the smooth solution to the problem (1.13)– (1.15) (4.8). It follows from the Lp-theory of parabolic system ( [7]) that Lemma 2.5 with Ω replaced by Qε also holds. Moreover, for T>0 and p∈ (2,∞),Theorem 2.1 ”
- A structurally damped plate equation with Dirichlet-Neumann boundary conditions (2015, methodology): “5 of [11] (see also the proof of Lemma 3.”
- Traces and embeddings of anisotropic function spaces (2012, positive): “1) was obtained in [43, 44] for q ≤ p and more general cases were considered in [10, 21].”