Results 31 to 40 of about 259 (139)
The Boundary Value Problem of the Equations with Nonnegative Characteristic Form
Boundary Value Problems, 2010 We study the generalized Keldys-Fichera boundary value problem for a class of higher order equations with nonnegative characteristic. By using the acute angle principle and the Hölder inequalities and Young inequalities we discuss the existence of ...
Li Limei, Ma Tian
doaj +2 more sources
Trace theorems on Herz-Morrey spaces with applications to Sobolev type inequalities
Boundary Value ProblemsIn this paper, we prove the trace theorems in the setting of Riesz potential operator for Herz-Morrey spaces and present some examples to illustrate the optimality of certain parametric conditions.
Abdul Hamid Ganie +4 more
doaj +1 more source
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. +1 more
openaire +2 more sources
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 +2 more
wiley +1 more source
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
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 Dual Hamilton–Jacobi Equation and the Poincaré Inequality
MathematicsFollowing the equivalence between logarithmic Sobolev inequalities and hypercontractivity shown by L. Gross, and applying the ideas and methods of the work by Bobkov, Gentil and Ledoux, we would like to establish a new connection between the logarithmic ...
Rigao He +3 more
doaj +1 more source
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
The Limiting Cases of Affine Hardy–Littlewood–Sobolev Inequalities
AxiomsIn this paper, we studied the limiting regimes α→n− and α→0+ in the affine Hardy–Littlewood–Sobolev (HLS) inequalities. Specifically, we established affine logarithmic HLS inequalities and affine Beckner-type logarithmic Sobolev inequalities for pairs of
Youjiang Lin, Jiaming Lan, Jinghong Zhou
doaj +1 more source
Sobolev type inequalities for compact metric graphs
Journal of Inequalities and Applications, 2018 In this paper analogues of Sobolev inequalities for compact and connected metric graphs are derived. As a consequence of these inequalities, a lower bound, commonly known as Cheeger inequality, on the first non-zero eigenvalue of the Laplace operator ...
Muhammad Usman
doaj +1 more source