Results 31 to 40 of about 2,173 (142)
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
doaj +1 more source
Traces and fractional Sobolev extension domains with variable exponent
, 2018 Assume that Ω ⊂ RN is a bounded domain of class C0,1 and denoted by Ws,q(.),p(.,.) (Ω) the fractional Sobolev space with variable exponent. We show that Ω is a Ws,q(.),p(.,.)−extension domain for s ∈ (0, 1).
A. Baalal, Mohamed Berghout
semanticscholar +1 more source
Hardy inequalities and Caffarelli-Kohn-Nirenberg inequalities with radial derivative
Journal of Mathematical Inequalities, 2020 In this paper, we study several inequalities of Hardy and Caffarelli-Kohn-Nirenberg type. We set up some optimal versions of these inequalities using the radial derivatives or the convex combinations of the full gradient and its radial part.
Tuan Duy Nguyen, L. Phi, W. Yin
semanticscholar +1 more source
On extremals for the Trudinger-Moser inequality with vanishing weight in the N-dimensional unit ball
, 2020 In this paper, we study the extremal function for the Trudinger-Moser inequality with vanishing weight in the unit ball B⊂RN (N 3). To be exact, let S be the set of all decreasing radially symmetrical functions and αN = Nω 1/(N−1) N−1 , where ωN−1 is the
Mengjie Zhang
semanticscholar +1 more source
On the trace space of a Sobolev space with a radial weight
Journal of Function Spaces, Volume 6, Issue 3, Page 259-276, 2008., 2008 Our concern in this paper lies with trace spaces for weighted Sobolev spaces, when the weight is a power of the distance to a point at the boundary. For a large range of powers we give a full description of the trace space.
Helmut Abels +3 more
wiley +1 more source
A homogeneity property for Besov spaces
Journal of Function Spaces, Volume 5, Issue 2, Page 123-132, 2007., 2007 A homogeneity property for some Besov spaces Bp,qs is proved. An analogous property for some Fp,qs spaces is already known.
António M. Caetano +3 more
wiley +1 more source
The Lusin Theorem and Horizontal Graphs in the Heisenberg Group
Analysis and Geometry in Metric Spaces, 2013 In this paper we prove that every collection of measurable functions fα , |α| = m, coincides a.e. withmth order derivatives of a function g ∈ Cm−1 whose derivatives of order m − 1 may have any modulus of continuity weaker than that of a Lipschitz ...
Hajłasz Piotr, Mirra Jacob
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Zero-order Mehler-Fock transform and Sobolev-type space
Mathematical Inequalities & Applications, 2019 The present paper is devoted to the study of the Mehler-Fock transform with index as the Legendre function of first kind. Continuity property of the Mehler-fock transform on the test function spaces Λα and Gα is given.
A. Prasad, U. K. Mandal, S. Verma
semanticscholar +1 more source
Logarithmic Sobolev inequality revisited [PDF]
, 2017 We provide a new characterization of the logarithmic Sobolev inequality.Comment: 5 ...
Nguyen, Hoai-Minh, Squassina, Marco
core +5 more sources
Trace theorems for Sobolev‐Slobodeckij spaces with or without weights
Journal of Function Spaces, Volume 5, Issue 3, Page 243-268, 2007., 2007 We prove that the well‐known trace theorem for weighted Sobolev spaces holds true under minimal regularity assumptions on the domain. Using this result, we prove the existence of a bounded linear right inverse of the trace operator for Sobolev‐Slobodeckij spaces Wps(Ω) when s − 1/p is an integer.
Doyoon Kim, Hans Triebel
wiley +1 more source