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Improved Hardy inequalities with exact remainder terms
, 2020 We set up several identities that imply some versions of the Hardy type inequalities. These equalities give a straightforward understanding of several Hardy type inequalities as well as the nonexistence of nontrivial optimizers.
Tuan Duy Nguyen +3 more
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Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, I [PDF]
, 2004 36 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.-- Part II of this paper published in: Approx. Theory Appl. 18(2): 1-32 (2002), available at: http://e-archivo.uc3m.es/handle/10016/6483MR#: MR2047389 (2005k:42062)Zbl#: Zbl 1081.42024In this ...
Pestana, Domingo +3 more
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Small perturbations of critical nonlocal equations with variable exponents
Demonstratio Mathematica, 2023 In this article, we are concerned with the following critical nonlocal equation with variable exponents: (−Δ)p(x,y)su=λf(x,u)+∣u∣q(x)−2uinΩ,u=0inRN\Ω,\left\{\begin{array}{ll}{\left(-\Delta )}_{p\left(x,y)}^{s}u=\lambda f\left(x,u)+{| u| }^{q\left(x)-2}u&
Tao Lulu, He Rui, Liang Sihua
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Trace Operators on Regular Trees
Analysis and Geometry in Metric Spaces, 2020 We consider different notions of boundary traces for functions in Sobolev spaces defined on regular trees and show that the almost everywhere existence of these traces is independent of the chosen definition of a trace.
Koskela Pekka +2 more
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Moroccan Journal of Pure and Applied Analysis, 2021 We prove in this paper some existence and unicity results of entropy and renormalized solutions for some nonlinear elliptic equations with general anisotropic diffusivities and variable exponents. The data are assumed to be merely integrable.
Moumni Mostafa El, Mohamed Deval Sidi
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A note on truncations in fractional Sobolev spaces [PDF]
, 2017 We study the Nemytskii operators $u\mapsto |u|$ and $u\mapsto u^{\pm}$ in fractional Sobolev spaces $H^s(\mathbb R^n)$, $s>1$.Comment: 9 ...
Musina, Roberta, Nazarov, Alexander I.
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A note on the fractional perimeter and interpolation [PDF]
, 2017 We present the fractional perimeter as a set-function interpolation between the Lebesgue measure and the perimeter in the sense of De Giorgi. Our motivation comes from a new fractional Boxing inequality that relates the fractional perimeter and the ...
Ponce, Augusto C., Spector, Daniel
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Optimality of Serrin type extension criteria to the Navier-Stokes equations
Advances in Nonlinear Analysis, 2021 We prove that a strong solution u to the Navier-Stokes equations on (0, T) can be extended if either u ∈ Lθ(0, T; U˙∞,1/θ,∞−α$\begin{array}{} \displaystyle \dot{U}^{-\alpha}_{\infty,1/\theta,\infty} \end{array}$) for 2/θ + α = 1, 0 < α < 1 or u ∈ L2(0, T;
Farwig Reinhard, Kanamaru Ryo
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Sobolev subspaces of nowhere bounded functions [PDF]
, 2016 We prove that in any Sobolev space which is subcritical with respect to the Sobolev Embedding Theorem there exists a closed infinite dimensional linear subspace whose non zero elements are nowhere bounded functions.
Lamberti, PIER DOMENICO +1 more
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Multivariate Analogue of Slant Toeplitz Operators
Hacettepe Journal of Mathematics and Statistics, 2020 This paper discusses several structural and fundamental properties of the kth-order slant Toeplitz operators on the Lebesgue space of the ntorus Tn, for integers k ≥ 2 and n ≥ 1. We obtain certain equivalent conditions for the commutativity and essential
Gopal Datt, Shesh Kumar Pandey
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