Results 71 to 80 of about 5,037 (196)

Concentrated solutions for a fractional Choquard-type Brézis–Nirenberg problem

Bulletin of Mathematical Sciences
This paper is devoted to investigating the following fractional Choquard-type Brézis–Nirenberg problem (−Δ)su=∫Ωu2α,s∗(y)|x−y|αdyu2α,s∗−1+𝜀uin Ω,u>0in Ω,u=0in ℝN\Ω, where [Formula: see text], [Formula: see text] denotes the fractional Laplacian, [Formula:
Shengbing Deng, Wenshan Luo
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

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

An optimal Hardy-Littlewood-Sobolev inequality on $\mathbf R^{n-k} \times \mathbf R^n$ and its consequences

, 2023
For $n > k \geq 0$, $\lambda >0$, and $p, r>1$, we establish the following optimal Hardy-Littlewood-Sobolev inequality \[ \Big| \iint_{\mathbf R^n \times \mathbf R^{n-k}} \frac{f(x) g(y)}{ |x-y|^\lambda |y"|^\beta} dx dy \Big| \lesssim \| f \| _{L^p ...
Nguyen, Quoc-Hung, Ngô, Quôc Anh, Nguyen, Van Hoang   +2 more
core  

Optimality of embeddings in Orlicz spaces

Mathematische Nachrichten, Volume 298, Issue 7, Page 2380-2400, July 2025.
Abstract Working with function spaces in various branches of mathematical analysis introduces optimality problems, where the question of choosing a function space both accessible and expressive becomes a nontrivial exercise. A good middle ground is provided by Orlicz spaces, parameterized by a single Young function and thus accessible, yet expansive ...
Tomáš Beránek
wiley   +1 more source

On the integral systems related to Hardy-Littlewood-Sobolev inequality [PDF]

Mathematical Research Letters, 2007
We prove all the maximizers of the sharp Hardy-Littlewood-Sobolev inequality are smooth. More generally, we show all the nonnegative critical functions are smooth, radial with respect to some points and strictly decreasing in the radial direction.
openaire   +2 more sources

The free boundary for semilinear problems with highly oscillating singular terms

Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.
Abstract We investigate general semilinear (obstacle‐like) problems of the form Δu=f(u)$\Delta u = f(u)$, where f(u)$f(u)$ has a singularity/jump at {u=0}$\lbrace u=0\rbrace$ giving rise to a free boundary. Unlike many works on such equations where f$f$ is approximately homogeneous near {u=0}$\lbrace u = 0\rbrace$, we work under assumptions allowing ...
Mark Allen, Dennis Kriventsov, Henrik Shahgholian   +2 more
wiley   +1 more source

Reversed Hardy-Littewood-Sobolev inequality [PDF]

, 2020
In this paper, we obtain a reversed Hardy-Littlewood-Sobolev inequality: for 0 < p, t < 1 and λ = n − α < 0 with 1/p + 1/t + λ/n = 2, there is a best constant N (n, λ, p) > 0, such that For p = t, we prove the existence of extremal functions,
Meijun Zhu, Jingbo Dou
core  

Estimates for smooth Weyl sums on minor arcs

Bulletin of the London Mathematical Society, Volume 57, Issue 3, Page 657-668, March 2025.
Abstract We provide new estimates for smooth Weyl sums on minor arcs and explore their consequences for the distribution of the fractional parts of αnk$\alpha n^k$. In particular, when k⩾6$k\geqslant 6$ and ρ(k)$\rho (k)$ is defined via the relation ρ(k)−1=k(logk+8.02113)$\rho (k)^{-1}=k(\log k+8.02113)$, then for all large numbers N$N$ there is an ...
Jörg Brüdern, Trevor D. Wooley
wiley   +1 more source

Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials [PDF]

, 2011
We deal with nonnegative distributional supersolutions for a class of linear elliptic equations involving inverse-square potentials and logarithmic weights.
Roberta Musina, Fall, Mouhamed Moustapha, Musina Roberta, Fall MouhamedMoustapha, FALL MM, Musina, Roberta, Mouhamed Moustapha Fall, MouhamedMoustapha Fall, Fall, Mm   +8 more
core   +1 more source