Results 41 to 50 of about 792 (140)

The bounded variation capacity and Sobolev-type inequalities on Dirichlet spaces

Advances in Nonlinear Analysis
In this article, we consider the bounded variation capacity (BV capacity) and characterize the Sobolev-type inequalities related to BV functions in a general framework of strictly local Dirichlet spaces with a doubling measure via the BV capacity.
Xie Xiangyun, Liu Yu, Li Pengtao, Huang Jizheng   +3 more
doaj   +1 more source

Heat-Semigroup-Based Besov Capacity on Dirichlet Spaces and Its Applications

Mathematics
In this paper, we investigate the Besov space and the Besov capacity and obtain several important capacitary inequalities in a strictly local Dirichlet space, which satisfies the doubling condition and the weak Bakry–Émery condition.
Xiangyun Xie, Haihui Wang, Yu Liu
doaj   +1 more source

Existence of Weak Solutions for the Equations of a Non‐Newtonian Fluid With Non‐Standard Growth

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 106, Issue 7, July 2026.
ABSTRACT We consider the equations of a non‐Newtonian incompressible fluid in a general time‐space cylinder ΩT=Ω×(0,T)⊂Rn×R,n≥2$\Omega _{T} = \Omega \times (0,T) \subset \mathbb {R}^{n} \times \mathbb {R}, n \ge 2$. We assume that the rheology of the fluid is changing with respect to time and space, and satisfies, for each (x,t)∈ΩT$(x,t) \in \Omega _{T}
Hyeong‐Ohk Bae, Jörg Wolf
wiley   +1 more source

Characterizations of Orlicz-Sobolev Spaces by Means of Generalized Orlicz-Poincaré Inequalities

Journal of Function Spaces and Applications, 2012
Let Φ be an N-function. We show that a function u∈LΦ(ℝn) belongs to the Orlicz-Sobolev space W1,Φ(ℝn) if and only if it satisfies the (generalized) Φ-Poincaré inequality. Under more restrictive assumptions on Φ, an analog of the result holds in a general
Toni Heikkinen
doaj   +1 more source

A relative Poincaré–Birkhoff theorem

Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.
Abstract A. Moreno and Otto van Koert proved a generalised version of the classical Poincaré–Birkhoff theorem, for Liouville domains of any dimension. In this article, we prove a relative version for Lagrangians with Legendrian boundary. This gives interior chords of arbitrary large length, provided that the twist condition introduced by Moreno and van
Agustin Moreno, Arthur Limoge
wiley   +1 more source

Poincaré Inequalities for Mutually Singular Measures

Analysis and Geometry in Metric Spaces, 2015
Using an inverse system of metric graphs as in [3], we provide a simple example of a metric space X that admits Poincaré inequalities for a continuum of mutually singular measures.
Schioppa Andrea
doaj   +1 more source

Simple normal crossing Kähler–Einstein metrics and RCD spaces

Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.
Abstract We show that Kähler–Einstein metrics with cone singularities along simple normal crossing (SNC) divisors define Riemannian Curvature Dimension (RCD) spaces, both in the compact setting and in certain non‐compact cases, thereby producing many examples of Einstein RCD spaces. In particular, we show the existence of smooth non‐compact 4‐manifolds
Martin de Borbon, Cristiano Spotti
wiley   +1 more source

Duality of Moduli and Quasiconformal Mappings in Metric Spaces

Analysis and Geometry in Metric Spaces, 2020
We prove a duality relation for the moduli of the family of curves connecting two sets and the family of surfaces separating the sets, in the setting of a complete metric space equipped with a doubling measure and supporting a Poincaré inequality.
Jones Rebekah, Lahti Panu
doaj   +1 more source

From points to complexes: A concept of unexpectedness for simplicial complexes

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract In 2018, Cook, Harbourne, Migliore, and Nagel introduced the concept of unexpected hypersurfaces, which connects the study of Lefschetz properties of Artinian algebras defined by powers of linear forms to a family of interpolation problems.
Thiago Holleben
wiley   +1 more source

The Dual Hamilton–Jacobi Equation and the Poincaré Inequality

Mathematics
Following the equivalence between logarithmic Sobolev inequalities and hypercontractivity shown by L. Gross, and applying the ideas and methods of the work by Bobkov, Gentil and Ledoux, we would like to establish a new connection between the logarithmic ...
Rigao He, Wei Wang, Jianglin Fang, Yuanlin Li   +3 more
doaj   +1 more source