Results 31 to 40 of about 1,128 (190)

On Korn-Maxwell-Sobolev inequalities

Journal of Mathematical Analysis and Applications, 2021
We establish a family of inequalities that allow one to estimate the $\mathrm{L}^{q}$-norm of a matrix-valued field by the $\mathrm{L}^{q}$-norm of an elliptic part and the $\mathrm{L}^{p}$-norm of the matrix-valued curl. This particularly extends previous work by Neff et al. and, as a main novelty, is applicable in the regime $p=1$.
Franz Gmeineder, Daniel Spector
openaire   +3 more sources

The logarithmic Sobolev inequality on the Heisenberg group and applications to the uncertainty inequality and heat equation

Journal of Inequalities and Applications
We consider the logarithmic Sobolev inequality on the Heisenberg group. One can derive the logarithmic Sobolev inequality from the Sobolev inequality, and we consider an application to the uncertainty inequality on the Heisenberg group. Moreover, one can
Takeshi Suguro
doaj   +1 more source

Stability of Viscous Three‐Dimensional Stratified Couette Flow via Dispersion and Mixing

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT This article explores the stability of stratified Couette flow in the viscous 3d$3d$ Boussinesq equations. In this system, mixing effects arise from the shearing background, and gravity acts as a restoring force leading to dispersive internal gravity waves.
Michele Coti Zelati, Augusto Del Zotto, Klaus Widmayer   +2 more
wiley   +1 more source

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.
Przemysław Górka
doaj   +1 more source

Front Propagation Through a Perforated Wall

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki, François Hamel, Hiroshi Matano   +2 more
wiley   +1 more source

A Geometric Characterization of Steady Laminar Flow

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We study the steady states of the Euler equations on the periodic channel or annulus. We show that if these flows are laminar (layered by closed non‐contractible streamlines which foliate the domain), then they must be either parallel or circular flows.
Theodore D. Drivas, Marc Nualart
wiley   +1 more source

The affine Sobolev inequality

Journal of Differential Geometry, 1999
The author proves a new Sobolev inequality which is stronger than its classical, Euclidean counterpart. The main theorem in the article states, in fact, that if \(f\) is a \(C^1\) function with compact support in \(\mathbb{R}^n\), then \[ {1\over n} \int_{S^{n-1}} \|\nabla_u f\|^{-n}_1du\leq c_n\| f\|^{-n}_{{n\over n-1}}, \] where \(\nabla_u f\) is the
openaire   +2 more sources

Sobolev interpolation inequalities with weights [PDF]

Transactions of the American Mathematical Society, 1991
We study weighted local Sobolev interpolation inequalities of the form \[ 1
Gutierrez, Christian E., Wheeden, Richard L.   +1 more
openaire   +2 more sources

Weighted Rellich Inequality on H-Type Groups and Nonisotropic Heisenberg Groups

Journal of Inequalities and Applications, 2010
We prove a sharp weighted Rellich inequality associated with a class of Greiner-type vector fields on H-type groups. We also obtain some weighted Hardy- and Rellich-type inequalities on nonisotropic Heisenberg groups.
Yongyang Jin, Yazhou Han
doaj   +2 more sources

Kernel Bounds for Parabolic Operators Having First‐Order Degeneracy at the Boundary

Mathematische Nachrichten, EarlyView.
ABSTRACT We study kernel estimates for parabolic problems governed by singular elliptic operators ∑i,j=1N+1qijDij+cDyy,cγ+1>0,γ=qN+1,N+1,$$\begin{equation*} \sum _{i,j=1}^{N+1}q_{ij}D_{ij}+c\frac{D_y}{y},\qquad \frac{c}{\gamma }+1>0, \quad \gamma =q_{N+1,N+1}, \end{equation*}$$in the half‐space R+N+1={(x,y):x∈RN,y>0}$\mathbb {R}^{N+1}_+=\lbrace (x,y ...
L. Negro, C. Spina
wiley   +1 more source