您当前的位置:首页 > 论文浏览

1. chinaXiv:201809.00178 [pdf]

Regularity for a minimum problem with free boundary in Orlicz spaces

Jun Zheng; Leandro S. Tavares; Claudianor O. Alves
分类: 数学 >> 数学(综合)

The aim of this paper is to study the heterogeneous optimization problem \begin{align*} \mathcal {J}(u)=\int_{\Omega}(G(|\nabla u|)+qF(u^+)+hu+\lambda_{+}\chi_{\{u>0\}} )\text{d}x\rightarrow\text{min}, \end{align*} in the class of functions $ W^{1,G}(\Omega)$ with $ u-\varphi\in W^{1,G}_{0}(\Omega)$, for a given function $\varphi$, where $W^{1,G}(\Omega)$ is the class of weakly differentiable functions with $\int_{\Omega}G(|\nabla u|)\text{d}x<\infty$. The functions $G$ and $F$ satisfy structural conditions of Lieberman's type that allow for a different behavior at $0$ and at $\infty$. Given functions $q,h$ and constant $\lambda_+\geq 0$, we address several regularities for minimizers of $\mathcal {J}(u)$, including local $C^{1,\alpha}-$, and local Log-Lipschitz continuities for minimizers of $\mathcal {J}(u)$ with $\lambda_+=0$, and $\lambda_+>0$ respectively. We also establish growth rate near the free boundary for each non-negative minimizer of $\mathcal {J}(u)$ with $\lambda_+=0$, and $\lambda_+>0$ respectively. Furthermore, under additional assumption that $F\in C^1([0,+\infty); [0,+\infty))$, local Lipschitz regularity is carried out for non-negative minimizers of $\mathcal {J}(u)$ with $\lambda_{+}>0$.

提交时间: 2018-09-23 点击量1776下载量294 评论 0

2. chinaXiv:201809.00180 [pdf]

Regularity in the two-phase free boundary problems under non-standard growth conditions

Jun Zheng
分类: 数学 >> 数学(综合)

In this paper, we prove several regularity results for the heterogeneous, two-phase free boundary problems $\mathcal {J}_{\gamma}(u)=\int_{\Omega}\big(f(x,\nabla u)+(\lambda_{+}(u^{+})^{\gamma}+\lambda_{-}(u^{-})^{\gamma})+gu\big)\text{d}x\rightarrow \text{min}$ under non-standard growth conditions. Included in such problems are heterogeneous jets and cavities of Prandtl-Batchelor type with $\gamma=0$, chemical reaction problems with $0<\gamma<1$, and obstacle type problems with $\gamma=1$. Our results hold not only in the degenerate case of $p> 2$ for $p-$Laplace equations, but also in the singular case of $1

提交时间: 2018-09-22 点击量1847下载量282 评论 0

3. chinaXiv:201809.00179 [pdf]

H\"{o}lder continuity of solutions to the $G$-Laplace equation

Jun Zheng; Yan Zhang
分类: 数学 >> 数学(综合)

We establish regularity of solutions to the $G$-Laplace equation $-\text{div}\ \bigg(\frac{g(|\nabla u|)}{|\nabla u|}\nabla u\bigg)=\mu$, where $\mu$ is a nonnegative Radon measure satisfying $\mu (B_{r}(x_{0}))\leq Cr^{m}$ for any ball $B_{r}(x_{0})\subset\subset \Omega$ with $r\leq 1$ and $m>n-1-\delta\geq 0$. The function $g(t)$ is supposed to be nonnegative and $C^{1}$-continuous in $[0,+\infty)$, satisfying $g(0)=0$, and for some positive constants $\delta$ and $g_{0}$, $\delta\leq \frac{tg'(t)}{g(t)}\leq g_{0}, \forall t>0$, that generalizes the structural conditions of Ladyzhenskaya-Ural'tseva for an elliptic operator.

提交时间: 2018-09-22 点击量210下载量210 评论 0

4. chinaXiv:201611.00721 [pdf]

A Note on Elliptic Coordinates

Sun, Che
分类: 数学 >> 数学(综合)

Explicit equations are obtained to convert Cartesian coordinates to elliptic coordinates, based on which an elliptic-coordinate function can be readily mapped on a uniform Cartesian mesh.Application to Kirchhoff vortex is provided.

提交时间: 2018-09-22 点击量10730下载量858 评论 0

5. chinaXiv:201809.00176 [pdf]

一类高阶非线性微分方程Lyapunov不等式

郭旭; 王浩帆; 郑军
分类: 数学 >> 数学(综合)

本文研究一类高阶非线性微分方程的Lyapunov 不等式,是对《Lyapunov-type inequalities for $\psi$-Laplacian equations》有关结论的进一步探讨和推广.

提交时间: 2018-09-18 点击量2106下载量363 评论 0

6. chinaXiv:201809.00116 [pdf]

The obstacle problem for non-coercive equations with lower order term and $L^1-$data

Jun Zheng
分类: 数学 >> 数学(综合)

The aim of this paper is to study the obstacle problem associated with an elliptic operator having degenerate coercivity, and with a low order term and $L^1-$data. We prove the existence of an entropy solution to the obstacle problem and show its continuous dependence on the $L^{1}-$data in $W^{1,q}(\Omega)$ with some $q>1$.

提交时间: 2018-09-13 点击量1729下载量240 评论 0

7. chinaXiv:201806.00016 [pdf]

Lyapunov-type inequalities for a class of nonlinear higher order differential equations

Jun Zheng; Haofan Wang
分类: 数学 >> 数学(综合)

In this work, we establish several Lyapunov-type inequalities for a class of nonlinear higher order differential equations having a form \begin{align*} (\psi(u^{(m)}(x)))'+\sum_{i=0}^nr_i(x)f_i(u^{(i)}(x))=0, %\ \ \ \ \text{or}\ \ \ \ (\psi(u^{(m)}))^{(m)}+r_i(x)f(u)=0, \end{align*} with anti-periodic boundary conditions, where $m> n\geq 0$ are integers, $\psi$ and $f_i (i=0,1,2,...,n)$ satisfy certain structural conditions such that the considered equations have general nonlinearities. The obtained inequalities are extensions and complements of the existing results in the literature.

提交时间: 2018-06-04 点击量3096下载量478 评论 0

8. chinaXiv:201805.00171 [pdf]

Lyapunov-type inequalities for ψ−Laplacian equations

Zheng, Jun; Guo, Xu
分类: 数学 >> 数学(综合)

In this work, we present several Lyapunov-type inequalities for a class of $\psi-$Laplacian equations of the form \begin{align*} (\psi(u'(x)))'+r(x)f(u(x))=0, \end{align*} with Dirichlet boundary conditions, where $\psi$ and $f$ satisfies certain structural conditions with general nonlinearities. We do not require any sub-multiplicative property of $\psi$, and any convexity of $\frac{1}{\psi(t)}$ or $\psi (t)t$ in the establishment of Lyapunov-type inequalities. The obtained inequalities can be seen as extensions and complements of the existing results in the literature.

提交时间: 2018-05-22 点击量2256下载量399 评论 0

9. chinaXiv:201712.02142 [pdf]

Upper bounds for Z$_1$-eigenvalues of generalized Hilbert tensors

孟娟; 宋义生
分类: 数学 >> 数学(综合)

In this paper, we introduce the concept of Z$_1$-eigenvalue to infinite dimensional generalized Hilbert tensors (hypermatrix) $\mathcal{H}_\lambda^{\infty}=(\mathcal{H}_{i_{1}i_{2}\cdots i_{m}})$, $$ \mathcal{H}_{i_{1}i_{2}\cdots i_{m}}=\frac{1}{i_{1}+i_{2}+\cdots i_{m}+\lambda},\ \lambda\in \mathbb{R}\setminus\mathbb{Z}^-;\ i_{1},i_{2},\cdots,i_{m}=0,1,2,\cdots,n,\cdots, $$ and proved that its $Z_1$-spectral radius is not larger than $\pi$ for $\lambda>\frac{1}{2}$, and is at most $\frac{\pi}{\sin{\lambda\pi}}$ for $\frac{1}{2}\geq \lambda>0$. Besides, the upper bound of $Z_1$-spectral radius of an $m$th-order $n$-dimensional generalized Hilbert tensor $\mathcal{H}_\lambda^n$ is obtained also, and such a bound only depends on $n$ and $\lambda$.

提交时间: 2017-12-12 点击量3123下载量632 评论 0

10. chinaXiv:201712.01969 [pdf]

红外成像灰度随距离变化的李群表达

李晨曦; 史泽林; 刘云鹏
分类: 物理学 >> 电磁学、光学、声学、传热、经典力学和流体动力学
分类: 数学 >> 数学(综合)

大气对红外辐射传输的影响引起的红外成像灰度变化,是红外目标跟踪应用需要应对的问题。本文的研究目的是对红外成像灰度变化规律进行李群建模,对设计高效、鲁棒的目标跟踪算法有重要意义。首先分析了红外辐射传输模型,并结合红外成像机理,得到红外成像灰度变化模型。进一步从理论上证明了大气影响下红外成像灰度变化规律符合李群结构,提出了红外图像灰度动态变化的一种非欧数学表征。最后根据红外成像灰度变化模型对不同环境下采集到的外场实验数据进行拟合,回归分析结果表明了该模型的准确性,进而说明了本文对红外成像灰度变化规律进行李群表达的合理性。

提交时间: 2017-11-26 点击量6176下载量1293 评论 0

12  尾页  转到  [2 页/ 15 条记录]