Perturbations of elliptic operators in chord arc domains

机译：和弦弧域中的椭圆算子的扰动

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We study the boundary regularity of solutions to divergence form operators which are small perturbations of operators for which the boundary regularity of solutions is known. An operator is a small perturbation of another operator if the deviation function of the coefficients satisfies a Carleson measure condition with small norm. We extend Escauriaza's result on Lipschitz domains to chord arc domains with small constant. In particular we prove that if L_1 is a small perturbation of L_0 and log ko has small BMO norm so does log k_1. Here k_i denotes the density of the elliptic measure of L_i with respect to the surface measure of the boundary of the domain.

机译：我们研究了解决方案的解决方案的边界规律，这是一种官方运营商的小扰动，其官能液的边界规律性是已知的。如果系数的偏差函数满足具有小规范的Carleson测量条件，则操作员是另一个操作员的小扰动。我们将Escauriada的结果扩展到Lipschitz领域，以常量小的弧形域。特别是我们证明如果L_1是L_0的小扰动，则Log Ko具有小的BMO规范，因此Log K_1。这里k_i表示关于域的边界的表面测量的L_I的椭圆度量的密度。

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《Conference on Harmonic Analysis and Partial Differential Equations》|2014年||共19页
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Emmanouil Milakis; Jill Pipher; Tatiana Toro;
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中图分类 O174.2-532;
关键词
condition; solutions; constant;

机译：条件;解决方案;常数;

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专利

1. PERTURBATIONS OF ELLIPTIC OPERATORS IN 1-SIDED CHORD-ARC DOMAINS. PART I: SMALL AND LARGE PERTURBATION FOR SYMMETRIC OPERATORS [J] . Cavero Juan, Hofmann Steve, Maria Martell Jose Transactions of the American Mathematical Society . 2019,第4期

机译：单面弦弧结构域中的椭圆形算子的扰动。第一部分：对称运算符小而大的扰动
2. Perturbations of elliptic operators in 1-sided chord-arc domains. Part II: Non-symmetric operators and Carleson measure estimates [J] . Juan Cavero, Steve Hofmann, Jos Mara Martell, Transactions of the American Mathematical Society . 2020,第11期

机译：单面弦弧结构域中的椭圆形算子的扰动。第二部分：非对称运算符和Carleson措施估计
3. ON STABILITY OF SQUARE ROOT DOMAINS FOR NON-SELF-ADJOINT OPERATORS UNDER ADDITIVE PERTURBATIONS [J] . Gesztesy Fritz, Hofmann Steve, Nichols Roger Mathematika: A Journal of Pure and Applied Mathematics . 2016,第Pta1期

机译：摄动条件下非自伴算子的平方根域稳定性
4. Perturbations of elliptic operators in chord arc domains [C] . Emmanouil Milakis, Jill Pipher, Tatiana Toro Conference on Harmonic Analysis and Partial Differential Equations . 2014

机译：和弦弧域中的椭圆算子的扰动
5. The Dirichlet and regularity problems for second order linear elliptic operators in bounded Lipschitz domains. [D] . Nguyen, Nguyen T. 2014

机译：有界Lipschitz域中二阶线性椭圆算子的Dirichlet和正则性问题。
6. Pseudo-monotone operators and nonlinear elliptic boundary value problems on unbounded domains [O] . Felix E. Browder 1977

机译：无界域上的伪单调算子和非线性椭圆边值问题
7. Perturbations of elliptic operators in chord arc domains. [O] . Emmanouil Milakis, Jill Pipher, Tatiana Toro 2016

机译：弦弧域中椭圆算子的扰动。
8. Principal Eigenvalue and Maximum Principle for Second-Order Elliptic Operators inGeneral Domains [R] . Berestycki, H., Nirenberg, L., Varadhan, S. R. 1994

机译：一般域中二阶椭圆算子的主特征值和最大值原理

Perturbations of elliptic operators in chord arc domains

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