Results 61 to 70 of about 1,988 (121)
An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces
Advances in Nonlinear Analysis, 2020 It is known that functions in a Sobolev space with critical exponent embed into the space of functions of bounded mean oscillation, and therefore satisfy the John-Nirenberg inequality and a corresponding exponential integrability estimate.
Martínez Ángel D., Spector Daniel
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Equivalence between Poly\'a-Szeg\H{o} and relative capacity inequalities under rearrangement
, 2014 The transformations of functions acting on sublevel sets that satisfy a P\'olya-Szeg\H{o} inequality are characterized as those being induced by transformations of sets that do not increase the associated capacity.Comment: 9 ...
A. Alvino +6 more
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The concentration-compactness principles for Ws,p(·,·)(ℝN) and application
Advances in Nonlinear Analysis, 2020 We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems ...
Ho Ky, Kim Yun-Ho
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Absolute continuity of the best Sobolev constant of a bounded domain
, 2012 Let $\lambda_{q}:=\inf{\Vert\nabla u\Vert_{L^{p}(\Omega)}^{p}/\Vertu\Vert_{L^{q}(\Omega)}^{p}:u\in W_{0}^{1,p}(\Omega)\setminus{0}} $, where $\Omega$ is a bounded and smooth domain of $\mathbb{R}^{N ...
Antonietti +10 more
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On functional reproducing kernels
Open Mathematics, 2023 We show that even if a Hilbert space does not admit a reproducing kernel, there could still be a kernel function that realizes the Riesz representation map.
Zhou Weiqi
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Open Mathematics, 2023 We deal with multiplicity of solutions to the following Schrödinger-Poisson-type system in this article: ΔHu−μ1ϕ1u=∣u∣2u+Fu(ξ,u,v),inΩ,−ΔHv+μ2ϕ2v=∣v∣2v+Fv(ξ,u,v),inΩ,−ΔHϕ1=u2,−ΔHϕ2=v2,inΩ,ϕ1=ϕ2=u=v=0,on∂Ω,\left\{\begin{array}{ll}{\Delta }_{H}u-{\mu }_{1}{
Li Shiqi, Song Yueqiang
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A remark on Besov spaces interpolation over the 2-adic group
, 2011 Motivated by a recent result which identifies in the special setting of the 2-adic group the Besov space $\dot{B}^{1,\infty}_{1}(\mathbb{Z}_2)$ with $BV(\mathbb{Z}_2)$, the space of function of bounded variation, we study in this article some functional ...
Chamorro, Diego
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A counterexample for Improved Sobolev Inequalities over the 2-adic group
, 2010 On the framework of the 2-adic group Z_2, we study a Sobolev-like inequality where we estimate the L^2 norm by a geometric mean of the BV norm and the Besov space B(-1,\infty,\infty) norm.
Chamorro, Diego
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On a critical Choquard-Kirchhoff p-sub-Laplacian equation in ℍn
Analysis and Geometry in Metric SpacesThis article is devoted to the study of a critical Choquard-Kirchhoff pp-sub-Laplacian equation on the entire Heisenberg group Hn{{\mathbb{H}}}^{n}, where the Kirchhoff function KK can be zero at zero, i.e., the equation can be degenerate, and involving ...
Liang Sihua +3 more
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Sharp Sobolev Inequalities via Projection Averages. [PDF]
J Geom Anal, 2021 Kniefacz P, Schuster FE.
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