Results 61 to 70 of about 6,369 (172)

First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet

Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1523-1608, September 2025.
Abstract For any p∈(1,∞)$p \in (1,\infty)$, we construct p$p$‐energies and the corresponding p$p$‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular ...
Mathav Murugan, Ryosuke Shimizu
wiley   +1 more source

On a critical Choquard-Kirchhoff p-sub-Laplacian equation in ℍn

Analysis and Geometry in Metric Spaces
This article is devoted to the study of a critical Choquard-Kirchhoff pp-sub-Laplacian equation on the entire Heisenberg group Hn{{\mathbb{H}}}^{n}, where the Kirchhoff function KK can be zero at zero, i.e., the equation can be degenerate, and involving ...
Liang Sihua, Pucci Patrizia, Song Yueqiang, Sun Xueqi   +3 more
doaj   +1 more source

Uniqueness on average of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature

Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1656-1702, September 2025.
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, Marco Pozzetta, Daniele Semola   +2 more
wiley   +1 more source

Well-posedness of Cauchy problem of fractional drift diffusion system in non-critical spaces with power-law nonlinearity

Advances in Nonlinear Analysis
In this article, we consider the global and local well-posedness of the mild solutions to the Cauchy problem of fractional drift diffusion system with higher-order nonlinearity. The main difficulty comes from the higher-order nonlinearity. Instead of the
Gu Caihong, Tang Yanbin
doaj   +1 more source

Functionals for Multilinear Fractional Embedding

, 2014
A novel representation is developed as a measure for multilinear fractional embedding. Corresponding extensions are given for the Bourgain-Brezis-Mironescu theorem and Pitt's inequality.
Beckner, William
core   +1 more source

Sobolev and Hardy-Littlewood-Sobolev inequalities: duality and fast diffusion [PDF]

Mathematical Research Letters, 2011
In the euclidean space of dimension d ≥ 3, Sobolev and Hardy-Littlewood-Sobolev inequalities can be related by duality. We investigate how to relate these inequalities using the flow of a fast diffusion equation. Up to a term which is needed for homogeneity reasons, the difference of the two terms in Sobolev's inequality can be seen as the derivative ...
openaire   +3 more sources

Principal frequency of clamped plates on RCD(0,N)${\sf RCD}(0,N)$ spaces: Sharpness, rigidity, and stability

Proceedings of the London Mathematical Society, Volume 131, Issue 2, August 2025.
Abstract We study fine properties of the principal frequency of clamped plates in the (possibly singular) setting of metric measure spaces verifying the RCD(0,N)${\sf RCD}(0,N)$ condition, that is, infinitesimally Hilbertian spaces with nonnegative Ricci curvature and dimension bounded above by N>1$N>1$ in the synthetic sense.
Alexandru Kristály, Andrea Mondino
wiley   +1 more source

Bifurcation results for the critical Choquard problem involving fractional p-Laplacian operator

Boundary Value Problems, 2018
By using an abstract critical point theorem based on a pseudo-index related to the cohomological index, we prove the bifurcation results for the critical Choquard problems involving fractional p-Laplacian operator: (−Δ)psu=λ|u|p−2u+(∫Ω|u|pμ,s∗|x−y|μdy)|u|
Yuling Wang, Yang Yang
doaj   +1 more source

Existence of ground state solutions for critical fractional Choquard equations involving periodic magnetic field

Advanced Nonlinear Studies, 2022
In this paper, we consider the following critical fractional magnetic Choquard equation: ε2s(−Δ)A∕εsu+V(x)u=εα−N∫RN∣u(y)∣2s,α∗∣x−y∣αdy∣u∣2s,α∗−2u+εα−N∫RNF(y,∣u(y)∣2)∣x−y∣αdyf(x,∣u∣2)uinRN,\begin{array}{rcl}{\varepsilon }^{2s}{\left(-\Delta )}_{A ...
Jin Zhen-Feng, Sun Hong-Rui, Zhang Jianjun   +2 more
doaj   +1 more source

Martingale Transforms and the Hardy-Littlewood-Sobolev Inequality for Semigroups [PDF]

Potential Analysis, 2016
We give a representation of the fractional integral for symmetric Markovian semigroups as the projection of martingale transforms and prove the Hardy-Littlewood-Sobolev(HLS) inequality based on this representation. The proof rests on a new inequality for a fractional Littlewood-Paley $g$-function.
openaire   +3 more sources