Weighted L~p-estimates for Elliptic Equations with Measurable Coefficients in Nonsmooth Domains

Sun-Sig Byun; Dian K. Palagachev

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Weighted L~p-estimates for Elliptic Equations with Measurable Coefficients in Nonsmooth Domains

机译：非光滑域中可测系数椭圆方程的加权L〜p估计

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We obtain a global weighted L~p estimate for the gradient of the weak solutions to divergence form elliptic equations with measurable coefficients in a nonsmooth bounded domain. The coefficients are assumed to be merely measurable in one variable and to have small BMO semi-norms in the remaining variables, while the boundary of the domain is supposed to be Reifenberg flat, which goes beyond the category of domains with Lipschitz continuous boundaries. As consequence of the main result, we derive global gradient estimate for the weak solution in the framework of the Morrey spaces which implies global H?lder continuity of the solution.

机译：对于非光滑有界域中具有可测量系数的椭圆型方程的弱解的梯度，我们获得了全局加权L〜p估计。假定这些系数仅是一个变量中的可测量值，而其余变量中的BMO半范数较小，而该域的边界应该是Reifenberg平坦的，这超出了具有Lipschitz连续边界的域的范畴。作为主要结果的结果，我们导出了在Morrey空间框架中的弱解的全局梯度估计，这意味着该解的全局Hilder连续性。

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《Potential analysis: An international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis》 |2014年第1期|共29页
作者
Sun-Sig Byun; Dian K. Palagachev;
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正文语种 eng
中图分类数学;
关键词
Elliptic equation; Measurable coefficients; Gradient estimates; Muckenhoupt weight; Weighted L~p space; Reifenberg flat domain; Morrey space;

机译：椭圆方程;可测系数;梯度估计;Muckenhoupt权重;加权L〜p空间;Reifenberg平坦域;Morrey空间;

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1. Weighted L~p-estimates for Elliptic Equations with Measurable Coefficients in Nonsmooth Domains [J] . Sun-Sig Byun, Dian K. Palagachev Potential analysis: An international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis . 2014,第1期

机译：非光滑域中可测系数椭圆方程的加权L〜p估计
2. Gradient estimates for elliptic systems with measurable coefficients in nonsmooth domains [J] . Byun S.-S., Ryu S., Wang L. Manuscripta mathematica . 2010,第1a2期

机译：非光滑域中具有可测量系数的椭圆系统的梯度估计
3. Elliptic equations with measurable nonlinearities in nonsmooth domains [J] . Byun Sun-Sig, Kim Youchan Advances in Mathematics . 2016,第Null期

机译：非光滑域中具有可测量非线性的椭圆方程
4. THE MIXED BOUNDARY VALUE PROBLEM FOR NONLINEAR NONDIVERGENCE ELLIPTIC SYSTEMS OF SECOND ORDER EQUATIONS WITH MEASURABLE COEFFICIENTS IN HIGHER DIMENSIONAL DOMAINS [C] . Dechang Chen, Guo Chun Wen International ISAAC Congress . 2003

机译：高尺寸域中可测量系数的二阶方程的非线性发光椭圆系统的混合边值问题
5. On fully nonlinear elliptic and parabolic equations in domains with VMO coefficients [D] . Li, Xu. 2013

机译：VMO系数在域中的完全非线性椭圆形和抛物线方程
6. The Dirichlet Problem for Linear Elliptic Equations of Arbitrary Even Order with Variable Coefficients [O] . Felix E. Browder 1952

机译：变系数任意偶数线性椭圆方程的Dirichlet问题。
7. Weighted $L^p$-estimates for elliptic equations with measurable coefficients in nonsmooth domains [O] . Byun, Sun-Sig, Palagachev, Dian K. 2012

机译：具有可测量的椭圆方程的加权$ L ^ p $ -estimates 非光滑域中的系数
8. Regularity of the Solutions for Elliptic Problems on Nonsmooth Domains in R3.Part 1. Countably Normed Spaces on Polyhedral Domains [R] . Guo, B., Babuska, I. 1995

机译：R3.part中非光滑域椭圆问题解的正则性1.多面体域上的可数赋范空间

Weighted L~p-estimates for Elliptic Equations with Measurable Coefficients in Nonsmooth Domains

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