Results 11 to 20 of about 698 (138)
Characterization of interpolation between Grand, small or classical Lebesgue spaces [PDF]
Nonlinear Analysis, 2018 In this paper, we show that the interpolation spaces between Grand, small or classical Lebesgue are so called Lorentz-Zygmund spaces or more generally $GΓ$-spaces. As a direct consequence of our results any Lorentz-Zygmund space $L^{a,r}({\rm Log}\, L)^β$, is an interpolation space in the sense of Peetre between either two Grand Lebesgue spaces or ...
Fiorenza, Alberto +4 more
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A direct approach to the duality of grand and small Lebesgue spaces [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2009 Let \(\mathcal{M}_{0}\) be the set of all Lebesgue measurable function in the interval \((0,1)\), finite a.e.\ in it and let \(\mathcal{M}_{0}^{+}\) be the class of all nonnegative functions of \(\mathcal{M}_{0}\). For \(f \in \mathcal{M}_{0}\), the decreasing rearrangement \(f^{*}\) of \(f\) is defined by \[ f^{*} = \inf\{ \lambda > 0: |\{x \in (0,1):
G. DI FRATTA, FIORENZA, ALBERTO
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Hölder Quasicontinuity in Variable Exponent Sobolev Spaces
Journal of Inequalities and Applications, 2007 We show that a function in the variable exponent Sobolev spaces coincides with a Hölder continuous Sobolev function outside a small exceptional set.
Katja Tuhkanen +2 more
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Bilateral Small Lebesgue Spaces
, 2009 19 ...
Ostrovsky, Eugene, Sirota, Leonid
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Solutions of an anisotropic nonlocal problem involving variable exponent
Advances in Nonlinear Analysis, 2013 The present paper deals with an anisotropic Kirchhoff problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain of ℝN ().
Avci Mustafa +2 more
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Analyticity and Existence of the Keller–Segel–Navier–Stokes Equations in Critical Besov Spaces
Advanced Nonlinear Studies, 2018 This paper deals with the Cauchy problem to the Keller–Segel model coupled with the incompressible 3-D Navier–Stokes equations. Based on so-called Gevrey regularity estimates, which are motivated by the works of Foias and Temam [20], we prove that the ...
Yang Minghua, Fu Zunwei, Liu Suying
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The Boundedness of Generalized Fractional Integral Operators on Small Morrey Spaces
Cauchy: Jurnal Matematika Murni dan AplikasiThe small Morrey space is the set of locally Lebesgue integrable functions with norm defined supremum over radius of ball . This paper aims to prove the boundedness properties of the generality of fractional integral operators in small Morrey spaces ...
Rizky Aziz Syaifudin +3 more
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Front Propagation Through a Perforated Wall
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki +2 more
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Kernel Bounds for Parabolic Operators Having First‐Order Degeneracy at the Boundary
Mathematische Nachrichten, EarlyView.ABSTRACT We study kernel estimates for parabolic problems governed by singular elliptic operators ∑i,j=1N+1qijDij+cDyy,cγ+1>0,γ=qN+1,N+1,$$\begin{equation*} \sum _{i,j=1}^{N+1}q_{ij}D_{ij}+c\frac{D_y}{y},\qquad \frac{c}{\gamma }+1>0, \quad \gamma =q_{N+1,N+1}, \end{equation*}$$in the half‐space R+N+1={(x,y):x∈RN,y>0}$\mathbb {R}^{N+1}_+=\lbrace (x,y ...
L. Negro, C. Spina
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Optimal Homogeneous ℒp$$ {\boldsymbol{\mathcal{L}}}_{\boldsymbol{p}} $$‐Gain Controller
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT Nonlinear ℋ∞$$ {\mathscr{H}}_{\infty } $$‐controllers are designed for arbitrarily weighted, continuous homogeneous systems with a focus on systems affine in the control input. Based on the homogeneous ℒp$$ {\mathcal{L}}_p $$‐norm, the input–output behavior is quantified in terms of the homogeneous ℒp$$ {\mathcal{L}}_p $$‐gain as a ...
Daipeng Zhang +3 more
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