Results 71 to 80 of about 6,369 (172)

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

Reversed Hardy-Littlewood-Sobolev inequalities with weights on the Heisenberg group

Advances in Nonlinear Analysis, 2023
In this article, we establish some reverse weighted Hardy-Littlewood-Sobolev inequalities on the Heisenberg group. We then show the existence of extremal functions for the above inequalities by combining the subcritical approach and the renormalization ...
Hu Yunyun
doaj   +1 more source

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

On the p-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity

Demonstratio Mathematica
In this article, we deal with the following pp-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity: M([u]s,Ap)(−Δ)p,Asu+V(x)∣u∣p−2u=λ∫RN∣u∣pμ,s*∣x−y∣μdy∣u∣pμ,s*−2u+k∣u∣q−2u,x∈RN,M({\left[u]}
Zhao Min, Song Yueqiang, Repovš Dušan D.   +2 more
doaj   +1 more source

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

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

Non degeneracy of the bubble in the critical case for non local equations

, 2013
We prove the nondegeneracy of the extremals of the fractional Sobolev inequality as solutions of a critical semilinear nonlocal equation involving the fractional ...
Davila, Juan, del Pino, Manuel, Sire, Yannick   +2 more
core   +3 more sources

Ground states of a non‐local variational problem and Thomas–Fermi limit for the Choquard equation

Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.
Abstract We study non‐negative optimisers of a Gagliardo–Nirenberg‐type inequality ∫∫RN×RN|u(x)|p|u(y)|p|x−y|N−αdxdy⩽C∫RN|u|2dxpθ∫RN|u|qdx2p(1−θ)/q,$$\begin{align*} & \iint\nolimits _{\mathbb {R}^N \times \mathbb {R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-\alpha }} dx\, dy\\ &\quad \leqslant C{\left(\int _{{\mathbb {R}}^N}|u|^2 dx\right)}^{p\theta } {\
Damiano Greco, Yanghong Huang, Zeng Liu, Vitaly Moroz   +3 more
wiley   +1 more source

The best constant in a weighted Hardy-Littlewood-Sobolev inequality [PDF]

Proceedings of the American Mathematical Society, 2007
We prove the uniqueness for the solutions of the singular nonlinear PDE system: (1) { − δ ( | x
Chen, Wenxiong, Li, Congming
openaire   +2 more sources

Global second‐order estimates in anisotropic elliptic problems

Proceedings of the London Mathematical Society, Volume 130, Issue 3, March 2025.
Abstract This work deals with boundary value problems for second‐order nonlinear elliptic equations in divergence form, which emerge as Euler–Lagrange equations of integral functionals of the Calculus of Variations built upon possibly anisotropic norms of the gradient of trial functions.
Carlo Alberto Antonini, Andrea Cianchi, Giulio Ciraolo, Alberto Farina, Vladimir Maz'ya   +4 more
wiley   +1 more source