Elliptic differential equations with coefficients measurable with respect to one variable and vmo with respect to the others

Kim D; Krylov NV

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Elliptic differential equations with coefficients measurable with respect to one variable and vmo with respect to the others

机译：椭圆微分方程的系数相对于一个变量可测量，而vmo可相对于另一个变量

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摘要

We prove the unique solvability of second order elliptic equations in nondivergence form in Sobolev spaces. The coefficients of the second order terms are measurable in one variable and VMO in other variables. From this result, we obtain the weak uniqueness of the Martingale problem associated with the elliptic equations.

机译：我们证明了Sobolev空间中非散度形式的二阶椭圆方程的唯一可解性。在一个变量中可测量二阶项的系数，而在其他变量中可测量VMO。从该结果，我们获得了与椭圆方程有关的the问题的弱唯一性。

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《SIAM Journal on Mathematical Analysis》 |2007年第2期|共18页
作者
Kim D; Krylov NV;
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原文格式 PDF
正文语种 eng
中图分类数学分析;
关键词
second order equations; vanishing mean oscillation; Martingale problem;

机译：二阶方程;消失的平均振动;Mart问题;

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专利

1. ELLIPTIC DIFFERENTIAL EQUATIONS WITH COEFFICIENTS MEASURABLE WITH RESPECT TO ONE VARIABLE AND VMO WITH RESPECT TO THE OTHERS [J] . DOYOON KIM, N. V. KRYLOV SIAM Journal on Mathematical Analysis . 2008,第2期

机译：关于一个变量可测量的椭圆型微分方程，对于其他变量可测量的椭圆型微分方程
2. Second-order elliptic equations with variably partially VMO coefficients [J] . N.V. Krylov Journal of Functional Analysis . 2009,第6期

机译：可变VMO系数的二阶椭圆方程
3. PROBLEM WITH INHOMOGENEOUS INTEGRAL TIME CONDITION FOR A PARTIAL DIFFERENTIAL EQUATION OF THE FIRST ORDER WITH RESPECT TO TIME AND OF INFINITE ORDER WITH RESPECT TO THE SPACE VARIABLES [J] . P. I. Kalenyuk, I.V.Kohut, Z. M. Nytrebych, Journal of Mathematical Sciences . 2014,第1期

机译：一阶与时间有关的一阶微分方程和与空间变量有关的一阶无穷微分方程的不均匀积分时间问题
4. Stability With Respect to Part of Variables of Nonlinear Differential Equations with Non-Instantaneous Impulses [C] . Snezhana Hristova, Radoslava Terzieva International Conference on Applications of Mathematics in Engineering and Economics . 2018

机译：具有非瞬时脉冲的非线性微分方程的一部分变量的稳定性
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. SECOND-ORDER ELLIPTIC EQUATIONS WITH VARIABLY PARTIALLY VMO COEFFICIENTS [O] . 2016

机译：具有可变部分VmO系数的二阶椭圆方程
8. Exact Solution of the Nonlinear Differential Equation R(2nd derivative R with respect to t) Plus (3/2)(dR/dt) squared-A(R sup 4) Plus B Equals 0 [R] . Childs, D. R. 1972

机译：非线性微分方程R的精确解（相对于t的二阶导数R）加（3/2）（dR / dt）平方-a（R sup 4）加B等于0

Elliptic differential equations with coefficients measurable with respect to one variable and vmo with respect to the others

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