Results 71 to 80 of about 1,988 (121)

Duality of capacities and Sobolev extendability in the plane. [PDF]

Complex Analysis Synerg, 2021
Zhang YR.
europepmc   +1 more source

Weighted Hardy-Adams inequality on unit ball of any even dimension

Advances in Nonlinear Analysis
In this study, we obtain the weighted Hardy-Adams inequality of any even dimension n≥4n\ge 4. Namely, for u∈C0∞(Bn)u\in {C}_{0}^{\infty }\left({{\mathbb{B}}}^{n}) with ∫Bn∣∇n2u∣2dx−∏k=1n⁄2(2k−1)2∫Bnu2(1−∣x∣2)ndx≤1,\mathop{\int }\limits_{{{\mathbb{B}}}^{n}
Wang Xumin
doaj   +1 more source

Nonexistence and existence of solutions for a supercritical p-Laplacian elliptic problem

Advanced Nonlinear Studies
In this paper, we obtain a general supercritical Sobolev inequality in W0,rad1,p(B) ${W}_{0,rad}^{1, p}\left(B\right)$ , where B is the unit ball in RN ${\mathbb{R}}^{N}$ .
Liu Yanjun, Li Yu, Chen Yuan
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A topological analysis of p(x)-harmonic functionals in one-dimensional nonlocal elliptic equations

Advanced Nonlinear Studies
We consider a class of one-dimensional elliptic equations possessing a p(x)-harmonic functional as a nonlocal coefficient.
Goodrich Christopher S.
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Singular Trudinger–Moser inequalities for the Aharonov–Bohm magnetic field

Advanced Nonlinear Studies
The first purpose of this paper is to establish the singular Trudinger–Moser inequality in R2 ${\mathbb{R}}^{2}$ for the Aharonov–Bohm magnetic fields.
Wang Xumin
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Anisotropic adams’ type inequality with exact growth in R4 ${\mathbb{R}}^{4}$

Advanced Nonlinear Studies
In this paper, we mainly extend the classical Adams’ inequality to its anisotropic type. By using the rearrangement argument, we establish best constants for anisotropic Adams’ type inequality with exact growth in R4 ${\mathbb{R}}^{4}$ .
Zhang Tao, Yang Fan, Cheng Tingzhi, Zhou Chunqin   +3 more
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Fractional Maximal Functions in Metric Measure Spaces

Analysis and Geometry in Metric Spaces, 2013
We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev ...
Heikkinen Toni, Lehrbäck Juha, Nuutinen Juho, Tuominen Heli   +3 more
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An Agmon-Allegretto-Piepenbrink principle for Schrödinger operators. [PDF]

Rev R Acad Cienc Exactas Fis Nat A Mat, 2022
Buccheri S, Orsina L, Ponce AC.
europepmc   +1 more source

Qualitative properties of solutions to the viscoelastic beam equation with damping and logarithmic nonlinear source terms

Advances in Nonlinear Analysis
In this article, we consider the initial-boundary value problem for a class of viscoelastic extensible beam equations with logarithmic source term, strong damping term, and weak damping term.
Gao Yanchao, Pan Bingbai
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An embedding norm and the Lindqvist trigonometric functions

Electronic Journal of Differential Equations, 2002
We shall calculate the operator norm $|T|_p$ of the Hardy operator $Tf = int_0^x f $, where $1le ple infty$. This operator is related to the Sobolev embedding operator from $W^{1,p}(0,1)/mathbb{C}$ into $W^p(0,1)/mathbb{C}$.
Christer Bennewitz, Yoshimi Saito
doaj