Results 71 to 80 of about 259 (139)

Well‐Posedness and Analyticity of Solutions to the Stationary MHD Equations

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 106, Issue 8, August 2026.
ABSTRACT We consider the stationary problem of the MHD equations in R3$\mathbb {R}^3$. The aim of this article is to show existence, uniqueness, regularity, and analyticity of solutions in the scaling invariant homogeneous Besov space Ḃp,q−1+3/p$\dot{B}^{-1 + 3/p}_{p, q}$ for 1⩽p<3$1 \leqslant p < 3$ and 1⩽q⩽∞$1 \leqslant q \leqslant \infty$.
Kento Sube
wiley   +1 more source

On Critical Cases of Sobolev′s Inequalities

Journal of Functional Analysis, 1995
The author presents a new form of the Trudinger-type inequality, and proves the following result: Let \(p\) and \(p'\) satisfy \(1/p+ 1/p'= 1\) with \(1< p< \infty\). Then there exist positive constants and such that for all \(f\in H^{n/p, p} (\mathbb{R}^n)\) with \(|(-\Delta )^{n/2p} |_{L^p}\leq 1\), \[ \int_{\mathbb{R}^n} (\exp (\alpha|f(x) |^{p'})- \
openaire   +2 more sources

Sharp Hardy–Sobolev inequalities

Comptes Rendus. Mathématique, 2004
Let Ω be a smooth bounded domain in R N , N ⩾ 3
Filippas, S., Maz'ya, V. G., Tertikas, A.   +2 more
openaire   +2 more sources

Self‐improving property for certain degenerate functionals with generalized Orlicz growth

Bulletin of the London Mathematical Society, Volume 58, Issue 8, August 2026.
Abstract We investigate a self‐improving property of variational integrals in a weighted framework under generalized Orlicz growth conditions. Assuming that the weight belongs to an appropriate Muckenhoupt class and the growth function satisfies standard structural conditions, we prove that the gradient of any local quasi‐minimizer has local higher ...
Vertti Hietanen, Mikyoung Lee
wiley   +1 more source

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

A Generalization of a Logarithmic Sobolev Inequality to the Hölder Class

Journal of Function Spaces and Applications, 2012
In a recent work of the author, a parabolic extension of the elliptic Ogawa type inequality has been established. This inequality is originated from the Brézis-Gallouët-Wainger logarithmic type inequalities revealing Sobolev embeddings in the critical ...
H. Ibrahim
doaj   +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

Estimates for capacities and traces of potentials

International Journal of Mathematics and Mathematical Sciences, 1984
It is shown that “isoperimetric” inequalities, relating measures and capacities, hold for all sets in ℝn if they are valid for all balls. As a corollary, the necessary and sufficient conditions for the continuity of some imbeddings of M. Riesz and Bessel
V. G. Maz'ja, S. P. Preobrazenskii
doaj   +1 more source

Doubling measure and regularity to K-quasiminimizers of double-phase energy

Advances in Nonlinear Analysis
We consider an integral functional involving the double-phase operator in a metric measure space equipped with a doubling measure. On the basis of suitable hypotheses on the function governing the phase changes, we design a unifying approach to establish
Cen Jinxia, Vetro Calogero, Zeng Shengda
doaj   +1 more source