Secondly, through integrating by parts and using Cauchy inequality, thanks to a lemma of Gronwalls type, an energy inequality is got and a priori estimate is established.

接下來經(jīng)過分部積分和Cauchy不等式，并利用Gronwall型引理得到一個能量不等式91欧美在线视频，對解的范數(shù)給出先驗估計无码精品视频在线观看。

Secondly, through integrating by parts and using Cauchy inequality, thanks to a lemma of Gronwall's type, an energy inequality is got and a priori estimate is established.

接下來經(jīng)過分部積分和Cauchy不等式，并利用Gronwall型引理得到一個能量不等式两个小姨子木瓜电影网，對解的范數(shù)給出先驗估計日本中文字幕的视频网站。

First, we establish an energy inequality in the case that no boundary conditions are imposed, and obtain a uniqueness result in the Cauchy problem for the model.

首先，對沒有任何邊界條件的方程給出一個能量不等式国产欧美日韩在线综合网，并且獲得Koiter殼的一個Cauchy問題的唯一性結(jié)果日本AⅤ永久免费网站WWW。

In the case of Dirichlet boundary conditions,these estimates were improved by Baker[1]who used a technique that can be interpreted as a nonstandard energy argument.

Dupont[15]使用標(biāo)準(zhǔn)能量方法給出了一類線性雙曲方程Galerkin解的L2誤差估計，對于Dirichlet型邊值問題久久精品视频99，Baker[1]對其結(jié)果作了改進(jìn)亚洲国产人自精在线尤物，用的是一種可謂"非標(biāo)準(zhǔn)的能量不等式"方法。

The paper first obtains the L2 -apriori estimates for the solutions of two kinds of autocatalytic model s under Dirichlet boundary conditions, and then, using the properties of linear semigroup and delicate calculations, the estimates of the maximal norms are obtained, therefore, the global existence of the solutions is proved.

該文利用重要不等式及能量積分方法首先得到了解的初等的先驗估計免费A级毛片全免费还看。然后利用線性半群的有關(guān)性質(zhì)及精細(xì)計算得到了解的最大模估計综合操逼网，從而證明了兩類三次自催化模型在Dirichlet邊界條件下整體解的存在性，并進(jìn)而證明了第一類模型的最大吸引子的存在性

The main aim of this thesis is to study the properties of the maps for Heisenberg group target, which include Lipschitz and Holder continuity, L~#,H~(n , W~(1,p)#,H~(n , BMO and John-Nirenberg estimates, embedded theorems, Poincare inequalities and reverse Poincare inequalities, the regul-arities about the minimizers.

本文的主要目的是系統(tǒng)研究靶流形為Heisenberg群的函數(shù)及其空間的性質(zhì)97超碰,人摸人人人澡人人，其中包括Lipschitz及Hlder連續(xù)性国产久在线视频观看、空間L~p及W~(1，p)的性質(zhì)天天夜碰日日摸日日澡、空間BMO的性質(zhì)及其上的John-Nirenberg估計黄色电影禁止18国产、嵌入定理、Poincare不等式和逆Poincare不等式亚洲自偷自偷偷色无码中文、能量極小映射的存在性新国模吧、正則性及用調(diào)和函數(shù)逼近能量極小映射等問題。

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundle For a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained.

中文摘要：本論文主要討論主叢上的規(guī)范固定Yang-Mills熱流我們在緊致無邊黎曼流形上的以半單緊致李群為結(jié)構(gòu)群的主叢上这里只精品视频，推導(dǎo)了在規(guī)范固定Yang-Mills熱流下曲率及其高階導(dǎo)數(shù)的演化方程欧美特黄在线视频，得到了該熱流的能量不等式和Bochner估計，由此可推出單調(diào)性公式和小作用量正則性插黄网站，以及曲率各階導(dǎo)數(shù)的局部一致估計天天碰天天日男人天堂。

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundleFor a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained. Then, the monotonicity formula and the small action regularity theorem can be proved. We will give the locally uniform estimates for the higher derivatives of the curvature.

本論文主要討論主叢上的規(guī)范固定Yang-Mills熱流我們在緊致無邊黎曼流形上的以半單緊致李群為結(jié)構(gòu)群的主叢上，推導(dǎo)了在規(guī)范固定Yang-Mills熱流下曲率及其高階導(dǎo)數(shù)的演化方程，得到了該熱流的能量不等式和Bochner估計性爱大黑吊网，由此可推出單調(diào)性公式和小作用量正則性99久久蜜v视频，以及曲率各階導(dǎo)數(shù)的局部一致估計。

The energy inequality and parabolic monotonici ty inequality is essential for the regularity of a weak solution to this problem .

該問題弱解的能量不等式和拋物單調(diào)不等式在證明弱解的正則性時起關(guān)鍵作用狠狠色2019。

The thesis consists of three parts:The first part deals with optimal Sobolev inequalities on compact Riemannian manifolds;the second part is concerned with some variational models in image processing,and we propose variational models as well as experimental results for detection,denoising and mosaicking;the last part deals with inverse differential geometry in 3-D non-local image restoration.

本論文由三個部分組成在线视频xxxx。第一部分是流形上的非線性分析：第二部分是基于能量極小化方法的圖像處理；第三部分是三維非局部圖像重建及逆向微分幾何欧美精品中文字幕手机在线。在第一部分中欧美A∨免费网站，我們研究了緊致流形上的最優(yōu)Sobolev不等式，證明了某些不等式雖然就整體而言是不成立的午夜三级理论福利电影，但總是局部成立的免费乱轮黄色网址。

energetic inequality：能量不等式

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