Results 81 to 90 of about 1,128 (190)

Brézis-Wainger Inequality on Riemannian Manifolds

Journal of Inequalities and Applications, 2008
The Brézis-Wainger inequality on a compact Riemannian manifold without boundary is shown. For this purpose, the Moser-Trudinger inequality and the Sobolev embedding theorem are applied.
Górka Przemysław
doaj  

KdV limit for the Vlasov–Poisson–Landau system

Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.
Abstract We are concerned with the fluid limit to KdV equations for the one‐dimensional Vlasov–Poisson–Landau system that describes the dynamics of ions in plasma with the electron density determined by the self‐consistent electric potential through the so‐called Boltzmann relation. Formally, it is well known that as the Knudsen number ε→0$\varepsilon \
Renjun Duan, Dongcheng Yang, Hongjun Yu
wiley   +1 more source

Weak Solutions for a Class of Nonlocal Singular Problems Over the Nehari Manifold

Mathematical Methods in the Applied Sciences, Volume 49, Issue 11, Page 12360-12378, 30 July 2026.
ABSTRACT In this paper, we consider a nonlocal model of dilatant non‐Newtonian fluid with a Dirichlet boundary condition. By using the Nehari manifold and fibering map methods, we obtain the existence of at least two weak solutions, with sign information.
Zhenfeng Zhang, Calogero Vetro, Tianqing An   +2 more
wiley   +1 more source

Sobolev Inequalities with Remainder Terms

Journal of Functional Analysis, 1985
Le résultat principal concerne l'inégalité de Sobolev \[ \int_{\Omega}| \nabla u|^ 2\geq S_ n\| u\|^ 2_{2^*}+C(\Omega)[u]^ 2_{2^*/2}. \] Pour toute fonction \(u\in H^ 1_ 0(\Omega)\), où \(\Omega \subset {\mathbb{R}}^ n\) est un ouvert borné, \(S_ n\) est la meilleure constante de Sobolev dans \({\mathbb{R}}^ n\), \(2^*={\mathfrak n}/(n-2)\) et [ \(]_ p\
Brezis, Haïm, Lieb, Elliott H.
openaire   +1 more source

Normalized solutions for a fractional coupled critical Hartree system

Electronic Journal of Qualitative Theory of Differential Equations
We consider the existence of normalized solutions for a fractional coupled Hartree system, with the upper critical exponent in the sense of the Hardy-Littelwood-Sobolev inequality.
Shengbing Deng, Wenshan Luo
doaj   +1 more source

The best constant of Sobolev inequality corresponding to anti-periodic boundary value problem

Electronic Journal of Qualitative Theory of Differential Equations, 2014
In this paper we establish the best constant of $\mathcal{L}^{p}$ Sobolev inequality for a function with anti-periodic boundary conditions. The best constant is expressed by $\mathcal{L}^q$ norm of $(M-1)$-th order Euler polynomial.
Jozef Kiseľák
doaj   +1 more source

A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin–Triebel spaces with mixed norms

Journal of Function Spaces and Applications, 2007
The article deals with a simplified proof of the Sobolev embedding theorem for Lizorkin–Triebel spaces (that contain the Lp-Sobolev spaces Hps as special cases).
Jon Johnsen, Winfried Sickel
doaj   +1 more source

Hardy–Sobolev interpolation inequalities

Calculus of Variations and Partial Differential Equations
AbstractWe derive a family of interpolation estimates which improve Hardy’s inequality and cover the Sobolev critical exponent. We also determine all optimizers among radial functions in the endpoint case and discuss open questions on nonrestricted optimizers.
Charlotte Dietze, Phan Thành Nam
openaire   +3 more sources

Poincaré and Log–Sobolev Inequalities for Mixtures [PDF]

Entropy, 2019
This work studies mixtures of probability measures on R n and gives bounds on the Poincaré and the log–Sobolev constants of two-component mixtures provided that each component satisfies the functional inequality, and both components are close in the χ 2 -distance.
openaire   +5 more sources