搜索结果: 1-15 共查到“偏微分方程 sobolev”相关记录15条 . 查询时间(0.063 秒)
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars："Sobolev extensions"(7)&(8)
Sobolev扩展 Whitney扩展 技术变体
2023/11/29
I will give an introduction to Sobolev extensions, including the use of variants of the Whitney extension technique. I will concentrate on the basics of the theory.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars："Sobolev extensions"(5)&(6)
Sobolev扩展 Whitney扩展 技术变体
2023/11/29
I will give an introduction to Sobolev extensions, including the use of variants of the Whitney extension technique. I will concentrate on the basics of the theory.
Absolute continuity of the best Sobolev constant of a bounded domain
Absolute continuity Lipschitz continuity p-Laplacian Rayleigh quotient Sobolev best constants
2012/6/7
Let $\lambda_{q}:=\inf{\Vert\nabla u\Vert_{L^{p}(\Omega)}^{p}/\Vertu\Vert_{L^{q}(\Omega)}^{p}:u\in W_{0}^{1,p}(\Omega)\setminus{0}} $, where $\Omega$ is a bounded and smooth domain of $\mathbb{R}^{N},...
On Control Of Sobolev Norms For Some Semilinear Wave Equations With Localized Data
Control Sobolev Norms Some Semilinear Wave Equations Localized Data
2012/4/16
We establish new bounds of the Sobolev norms of solutions of semilinear wave equations for data lying in the Hs, s<1, closure of compactly supported data inside a ball of radius R, with R a fixed and ...
Quasilinear elliptic equations and weighted Sobolev-Poincare inequalities with distributional weights
Quasilinear equations weighted integral inequalities elliptic regularity
2012/4/16
We introduce a class of weak solutions to the quasilinear equation $-\Delta_p u = \sigma |u|^{p-2}u$ in an open set $\Omega\subset\mathbf{R}^n$. Here $p>1$, and $\Delta_p u$ is the $p$-Laplacian opera...
On critical cases of Sobolev's inequalities for Heisenberg groups
Heisenberg group Sobolev's inequality Brezis-Gallouet-Wainger inequality
2011/10/17
This paper deal with the problem of Sobolev imbedding in the critical cases. We prove some Trudinger-type inequalities on the whole Heisenberg group, extending to this context the Euclidean results by...
Cauchy problem of nonlinear Schrodinger equation with initial data in Sobolev space W^{s,p} for p<2
Applied mathematics Cauchy problem nonlinear Schrodinger equation local well-posedness scaling limit
2011/10/15
In this paper, we consider in R^n the Cauchy problem for nonlinear Schrodinger equation with initial data in Sobolev space W^{s,p} for p<2. It is well known that this problem is ill posed. However, We...
On critical cases of Sobolev's inequalities for Carnot groups
Carnot group Sobolev's inequality Brezis-Gallouet-Wainger inequality
2011/10/15
In this paper we deal with the problem of Sobolev imbedding in thecritical cases on Carnot groups. We prove some Trudinger-type inequalities on the whole Carnot group, extending to this context the Eu...
Uniform Estimates of the Prolate Spheroidal Wave Functions and Spectral Approximation in Sobolev Spaces
Uniform Estimates of the Prolate Spheroidal Wave Functions Spectral Approximation Sobolev Spaces
2011/2/22
For fixed c Prolate Spheroidal Wave Functions ψn,c form a basis with remarkable properties
for the space of band-limited functions with bandwith c and have been largely studied and
used after the se...
Isoperimetric and Sobolev inequalities on hypersurfaces in sub-Riemannian Carnot groups
Carnot groups Sub-Riemannian Geometry Hypersurfaces Isoperimetric Inequality
2011/1/20
In this paper we shall study smooth submanifolds immersed in a k-step Carnot group G of homogeneous dimension Q. Our main result is an isoperimetric inequality for the case of a C2-smooth compact hype...
研究了一类含位势SobolevHardy极值函数, 这类函数是相应的最佳位势SobolevHardy常数的达到函数。运用巧妙细致的分析方法, 对这一类极值函数进行了截断误差估计, 这些估计结果对于研究带有含SobolevHardy临界项的椭圆方程解的存在性具有重要意义。
Heisenberg群上无穷远处的集中列紧原理和具有Sobolev临界指数的p - 次Laplace方程多解的存在性
Heisenberg 群 p -次Laplace算子 集中列紧原理 Palais-Smale条件 多解
2009/10/22
通过建立Heisenberg群上无穷远处的集中列紧原理, 研究了如下$p$ -次Laplace方程
-ΔH, pu=λg(ξ)|u|q-2u+f (ξ)|u|p*-2u, 在Hn上,
u ∈ D1, p(Hn),
其中ξ ∈ Hn, λ ∈ R, 1
近似惯性流形概念与耗散偏微分方程的长时间行为研究有关, 该文对非线性Sobolev Galpern方程构造了两个近似惯性流形. 证明了非平滑近似惯性流形Σ和平滑近似惯性流形Σ_0=P_mH对整体吸引子有相同的逼近阶数.
本文考虑了一类具Hardy-Sobolev临界指数的半线性椭圆方程, 通过证明局部{(P.S.)}条件和能量估计, 运用伪指标理论得到了这类方程多解的存在性.
Global Existence of Solutions for the Kawahara Equation in Sobolev Spaces of Negative Indices
Kawahara equation Cauchy problem global solution almost conservation law
2007/12/11
We first prove that the Cauchy problem of the Kawahara equation, $\partial_tu+u\partial_xu+\beta\partial_x^3u+\gamma\partial_x^5u=0,$ is locally solvable if the initial data belong to $H^{r}(\bf{R})...