Results 81 to 90 of about 5,040,927 (317)
Communications on Pure and Applied Mathematics, EarlyView.Abstract Let (Mn,g)$(M^n,g)$ be a complete Riemannian manifold which is not isometric to Rn$\mathbb {R}^n$, has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature decay. We prove that there exists a set G⊂(0,∞)$\mathcal {G}\subset (0,\infty)$ with density 1 at infinity such that for every V∈G$V\in \mathcal {G}$ there ...
Gioacchino Antonelli +2 more
wiley +1 more source
Variable Exponent Spaces of Differential Forms on Riemannian Manifold
Journal of Function Spaces and Applications, 2012 We introduce the Lebesgue space and the exterior Sobolev space for differential forms on Riemannian manifold 𝑀 which are the Lebesgue space and the Sobolev space of functions on 𝑀, respectively, when the degree of differential forms to be zero.
Yongqiang Fu, Lifeng Guo
doaj +1 more source
Duality properties of metric Sobolev spaces and capacity
Mathematics in Engineering, 2021 We study the properties of the dual Sobolev space $H^{-1,q}(\mathbb{X})= \big(H^{1,p}(\mathbb{X})\big)'$ on a complete extended metric-topological measure space $\mathbb{X}=(X,\tau,\rm{d},\rm{m})$ for $p\in (1,\infty)$.
Luigi Ambrosio, Giuseppe Savaré
doaj +1 more source
Nonlocal Gagliardo-Nirenberg-Sobolev type inequality [PDF]
arXiv, 2021 We establish Gagliardo-Nirenberg-Sobolev type inequalities on nonlocal Sobolev spaces driven by $p$-L\'{e}vy integrable kernels, by imposing some appropriate growth conditions on the associated critical function. This naturally allows to devise Sobolev embeddings, as well as, compact embeddings of nonlocal Sobolev spaces into Orlicz type spaces.
arxiv
The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space [PDF]
, 2007 It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the three dimensional upper half space is given by the Sobolev constant.
Benguria, Rafael D. +2 more
core +1 more source
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
Regularity and separation for Grušin‐type p‐Laplace operators
Mathematische Nachrichten, EarlyView.Abstract We analyze p‐Laplace type operators with degenerate elliptic coefficients. This investigation includes Grušin‐type p‐Laplace operators. We describe a separation phenomenon in elliptic and parabolic p‐Laplace type equations, which provide an illuminating illustration of simple jump discontinuities of the corresponding weak solutions ...
Daniel Hauer, Adam Sikora
wiley +1 more source
Clarkson’s Inequalities for Periodic Sobolev Space [PDF]
Учёные записки Казанского университета: Серия Физико-математические науки, 2016 The paper is devoted to developing the proof of Clarkson's inequalities for periodic functions belonging to the Sobolev space. The norm of the space has not been considered earlier.
I.V. Korytov
doaj
Dual Toeplitz Operators on the Orthogonal Complement of the Fock–Sobolev Space
Journal of Mathematics, 2023 In this paper, we consider the dual Toeplitz operators on the orthogonal complement of the Fock–Sobolev space and characterize their boundedness and compactness.
Li He, Biqian Wu
doaj +1 more source
Sobolev spaces, fine gradients and quasicontinuity on quasiopen sets
, 2015 We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space equipped with a doubling measure supporting a p-Poincar\'e inequality with ...
Björn, Anders +2 more
core +1 more source