共查询到20条相似文献,搜索用时 15 毫秒
1.
An Lq(Lp)-theory of divergence and non-divergence form parabolic equations is presented. The main coefficients are supposed to belong to the class VMOx, which, in particular, contains all measurable functions depending only on t. The method of proving simplifies the methods previously used in the case p=q. 相似文献
2.
We investigate the unique solvability of second order parabolic equations in non-divergence form in , p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition,
they are VMO (vanishing mean oscillation) with respect to the remaining variables.
The second author was partially supported by NSF Grant DMS-0140405. 相似文献
3.
Doyoon Kim 《Journal of Mathematical Analysis and Applications》2007,334(1):534-548
We prove the existence and uniqueness of solutions in Sobolev spaces to second-order parabolic equations in non-divergence form. The coefficients (except one of them) of second-order terms of the equations are measurable in both time and one spatial variables, and VMO (vanishing mean oscillation) in other spatial variables. 相似文献
4.
N.V. Krylov 《Journal of Functional Analysis》2009,257(6):1695-3327
The solvability in spaces is proved for second-order elliptic equations with coefficients which are measurable in one direction and VMO in the orthogonal directions in each small ball with the direction depending on the ball. This generalizes to a very large extent the case of equations with continuous or VMO coefficients. 相似文献
5.
YeMinCHEN 《数学学报(英文版)》2004,20(6):1103-1118
The aim of this paper is to study the regularity of solutions to the Dirichlet problems for general second-order elliptic equations in Lebesgue and Morrey spaces. We consider both nondivergence and divergence forms and the coefficients of principle terms are assumed to be in VMO. 相似文献
6.
Hongjie Dong 《分析论及其应用》2020,36(2):161-199
In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations. 相似文献
7.
本文给出了拟线性抛物型方程Cu=ut-aij(x,t,u)Diju+a(x,t,u,Du)=0在正则斜微商边界条件Bu=biDiu=g下的强解u∈Wq2,1(QT)(q>n+1)的存在、唯一性.这里我们假设系数aij是Caratheodory函数,且关于(x,t),aij∈VMO∩L∞;而函数a(x,t,u,Du)关于Du至多是二次增长. 相似文献
8.
In this paper, by means of the theories of singular integrals and linear commutators, the authors establish the regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients. 相似文献
9.
10.
11.
We study the obstacle problem with an elliptic operator in nondivergence form with principal coefficients in VMO. We develop all of the basic theory of existence, uniqueness, optimal regularity, and nondegeneracy of the solutions. These results, in turn, allow us to begin the study of the regularity of the free boundary, and we show existence of blowup limits, a basic measure stability result, and a measure-theoretic version of the Caffarelli alternative proven in [3]. 相似文献
12.
13.
We show continuity in generalized Morrey spaces of sublinear integral operators generated by Calderón-Zygmund operator and their commutators with BMO functions. The obtained estimates are used to study global regularity of the solution of the Dirichlet problem for linear uniformly elliptic operators. 相似文献
14.
建立了一类高阶非线性变系数函数方程一切解振动的几个充分条件,并且给出了在差分方程中的若干应用.结果全面推广了某些文献的结果. 相似文献
15.
16.
This paper concerns the convex optimal control problem governed by multiscale elliptic equations with arbitrarily rough $L^\infty$ coefficients, which has not only complex coupling between nonseparable scales and nonlinearity, but also important applications in composite materials and geophysics. We use one of the recently developed numerical homogenization techniques, the so-called Rough Polyharmonic Splines (RPS) and its generalization (GRPS) for the efficient resolution of the elliptic operator on the coarse scale. Those methods have optimal convergence rate which do not rely on the regularity of the coefficients nor the concepts of scale-separation or periodicity. As the iterative solution of the nonlinearly coupled OCP-OPT formulation for the optimal control problem requires solving the corresponding (state and co-state) multiscale elliptic equations many times with different right hand sides, numerical homogenization approach only requires one-time pre-computation on the fine scale and the following iterations can be done with computational cost proportional to coarse degrees of freedom. Numerical experiments are presented to validate the theoretical analysis. 相似文献
17.
A Maximum Principle for Elliptic and Parabolic Equations with Oblique Derivative Boundary Problems 下载免费PDF全文
Wang Lihe 《偏微分方程(英文版)》1992,5(4)
This paper prove a maximum principle for viscooity solutions of fully nonlinear, second order, uniformly elliptic and parabolic equations with oblique boundary value conditions. 相似文献
18.
具变系数时滞微分方程解的振动性 总被引:2,自引:0,他引:2
研究了时滞微分方程解的振动性,其中P(t)、τ(t)非负连续.我们证明了:如果对充分大的,且,则方程(*)每一解振动.该结论改进和推广了许多已知结果. 相似文献
19.
Space-time Estimates for Parabolic Type Operator and Application to Nonlinear Parabolic Equations 下载免费PDF全文
In this present paper we establish space-time estimates of solutions for linear parabolic type equations based on classical multipliers theory or operator semigroup theory. According to space-time estimates we first construct suitable work space L^q(0, T; L^P), moreover we study the Cauchy problem and initial boundary value problem for semilinear parabolic equation in L^q(0, T; L^P) type space. 相似文献
20.