Results 81 to 90 of about 85,041 (264)
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 +3 more
doaj +1 more source
Multiplicity results for logarithmic double phase problems via Morse theory
Bulletin of the London Mathematical Society, EarlyView.Abstract In this paper, we study elliptic equations of the form −divL(u)=f(x,u)inΩ,u=0on∂Ω,$$\begin{align*} -\operatorname{div}\mathcal {L}(u)=f(x,u)\quad \text{in }\Omega, \quad u=0 \quad \text{on } \partial \Omega, \end{align*}$$where divL$\operatorname{div}\mathcal {L}$ is the logarithmic double phase operator given by div|∇u|p−2∇u+μ(x)|∇u|q(e+|∇u ...
Vicenţiu D. Rădulescu +2 more
wiley +1 more source
Sobolev Spaces and Potential Spaces Associated to Hermite Polynomials Expansions
Extracta Mathematicae, 2018 The aim of this paper is to study the relation existing between potential spaces and Sobolev spaces, induced by the Ornstein-Uhlenbeck differential operator and associated to Hermite polynomials expansions, where we consider the multidimensional Gaussian
Iris A. López P.
doaj
Bulletin of the London Mathematical Society, EarlyView.Abstract We study standing waves of the Schrödinger equation with constant magnetic field and combined power nonlinearities, which describes a single non‐relativistic quantum particle in the presence of an electromagnetic field. We develop the local minima geometry method to establish the existence, estimates and mass collapse results for this equation,
Zhaosheng Feng, Yu Su
wiley +1 more source
Advanced Nonlinear Studies, 2019 In line with the Trudinger–Moser inequality in the fractional Sobolev–Slobodeckij space due to [S. Iula, A note on the Moser–Trudinger inequality in Sobolev–Slobodeckij spaces in dimension one, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.
Zhang Caifeng
doaj +1 more source
Sobolev spaces on Lipschitz curves [PDF]
Pacific Journal of Mathematics, 1996 We study Sobolev spaces on a Lipschitz graph \(\Gamma\) by means of a square function involving a geometric second difference. Given a function on the Sobolev space \(W^{1, p}(\Gamma)\) we show that the geometric square function is also in \(L^p(\Gamma)\).
openaire +4 more sources
The sharp Sobolev type inequalities in the Lorentz–Sobolev spaces in the hyperbolic spaces [PDF]
Journal of Mathematical Analysis and Applications, 2020 Let $W^1L^{p,q}(\mathbb H^n)$, $1\leq q,p < \infty$ denote the Lorentz-Sobolev spaces of order one in the hyperbolic spaces $\mathbb H^n$. Our aim in this paper is three-fold. First of all, we establish a sharp Poincar inequality in $W^1L^{p,q}(\mathbb H^n)$ with $1\leq q \leq p$ which generalizes the result in \cite{NgoNguyenAMV} to the setting ...
openaire +3 more sources
A fractal local smoothing problem for the wave equation
Bulletin of the London Mathematical Society, EarlyView.Abstract For any given set E⊂[1,2]$E\subset [1,2]$, we discuss a fractal frequency‐localized version of the Lp$L^p$ local smoothing estimates for the half‐wave propagator with times in E$E$. A conjecture is formulated in terms of a quantity involving the Assouad spectrum of E$E$ and the Legendre transform.
David Beltran +3 more
wiley +1 more source
Sobolev Spaces on Locally Compact Abelian Groups: Compact Embeddings and Local Spaces
Journal of Function Spaces, 2014 We continue our research on Sobolev spaces on locally compact abelian (LCA) groups motivated by our work on equations with infinitely many derivatives of interest for string theory and cosmology.
Przemysław Górka +2 more
doaj +1 more source
A characterization of nonhomogeneous wavelet dual frames in Sobolev spaces
Journal of Inequalities and Applications, 2016 In recent years, nonhomogeneous wavelet frames have attracted some mathematicians’ interest. This paper investigates such problems in a Sobolev space setting. A characterization of nonhomogeneous wavelet dual frames in Sobolev spaces pairs is obtained.
Jian-Ping Zhang, Yun-Zhang Li
doaj +1 more source