Sharp summability for Monge transport density via interpolation

Luigi De Pascale; Aldo Pratelli

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The $ℒ^{p, λ}$ spaces and applications to the theory of partial differential equations

Stampacchia, Guido

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Semivariation in $L^{p}$ -spaces

Brian Jefferies, Susumu Okada (2005)

Commentationes Mathematicae Universitatis Carolinae

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Suppose that $X$ and $Y$ are Banach spaces and that the Banach space $X {\hat{\otimes}}_{τ} Y$ is their complete tensor product with respect to some tensor product topology $τ$ . A uniformly bounded $X$ -valued function need not be integrable in $X {\hat{\otimes}}_{τ} Y$ with respect to a $Y$ -valued measure, unless, say, $X$ and $Y$ are Hilbert spaces and $τ$ is the Hilbert space tensor product topology, in which case Grothendieck’s theorem may be applied. In this paper, we take an index $1 \leq p < \infty$ and suppose that $X$ and $Y$ are $L^{p}$ -spaces with $τ_{p}$ the associated...

The scalar Oseen operator $- Δ + \partial / \partial x_{1}$ in $ℝ^{2}$

Chérif Amrouche, Hamid Bouzit (2008)

Applications of Mathematics

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This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in $L^{p}$ theory.

Stability for non-autonomous linear evolution equations with $L^{p}$ -maximal regularity

Hafida Laasri, Omar El-Mennaoui (2013)

Czechoslovak Mathematical Journal

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We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem $(P) \{\begin{matrix} \dot{u} (t) + A (t) u (t) = f (t) t -a.e. on [0, τ], u (0) = 0, \end{matrix}$ where $A : [0, τ] \to ℒ (X, D)$ is a bounded and strongly measurable function and $X$ , $D$ are Banach spaces such that $D \underset{d}{\to} ↪ X$ . Our main concern is to characterize $L^{p}$ -maximal regularity and to give an explicit approximation of the problem (P).

Displaying similar documents to “Sharp summability for Monge transport density via interpolation”

The ℒ p , λ spaces and applications to the theory of partial differential equations

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The scalar Oseen operator - Δ + ∂ / ∂ x 1 in ℝ 2

Stability for non-autonomous linear evolution equations with L p -maximal regularity

The $ℒ^{p, λ}$ spaces and applications to the theory of partial differential equations

Semivariation in $L^{p}$ -spaces

The scalar Oseen operator $- Δ + \partial / \partial x_{1}$ in $ℝ^{2}$

Stability for non-autonomous linear evolution equations with $L^{p}$ -maximal regularity