Oblique derivative problem for non-divergence parabolic equations with time-discontinuous coefficients

机译：具有时间不连续系数的非发散抛物型方程的倾斜衍生问题

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We consider an oblique derivative problem for non-divergence parabolic equations with discontinuous in t coefficients in a half-space. We obtain weighted coercive estimates of solutions in anisotropic Sobolev spaces. We also give an application of this result to linear parabolic equations in a bounded domain. In particular, if the boundary is of class C~(1,δ), δ ? (0,1], then we present a coercive estimate of solutions in weighted anisotropic Sobolev spaces, where the weight is a power of the distance to the boundary.

机译：我们考虑了在半空间中的T系数中不连续的非分歧抛物线方程的倾斜衍生问题。我们获得了各向异性SoboLev空间中解决方案的加权矫顽估计。我们还将此结果应用于有界域中的线性抛物线方程。特别地，如果边界是C〜（1，δ），δ？（0,1]，我们介绍了加权各向异性SoboLev空间中的溶液的矫顽估计，其中重量是与边界的距离的功率。

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《International Workshop on Advances in Mathematical Analysis of Partial Differential Equations》|2014年||共15页
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V. Kozlov; A. Nazarov;
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中图分类 O1-532;
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Non-divergence parabolic equations; discontinuous in time coefficients; oblique derivative problem; coercive estimates; anisotropic Sobolev spaces;

机译：非分歧抛物线方程;时间系数不连续;斜衍生物问题;强制性估计;各向异性Sobolev空间;

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专利

1. Oblique derivative problem for non-divergence parabolic equations with time-discontinuous coefficients in a wedge [J] . Kozlov Vladimir, Nazarov Alexander Journal of Mathematical Analysis and Applications . 2016,第1期

机译：楔中时间不连续系数的非散度抛物方程的斜导数问题
2. SOME INITIAL-OBLIQUE DERIVATIVE BOUNDARY VALUE PROBLEM FOR QUASILINEAR PARABOLIC EQUATIONS WITH UNBOUNDED COEFFICIENTS [J] . ZOU Benteng 系统科学与复杂性：英文版 . 2001,第003期

机译：具有无界系数的拟线性抛物型方程的某些初斜导数边值问题。
3. Initial-irregular oblique derivative problems for nonlinear parabolic complex equations of second order with measurable coefficients [J] . Wen GC., Zou BT. Nonlinear Analysis: An International Multidisciplinary Journal . 2000,第8期

机译：具有可测系数的二阶非线性抛物型复方程的初次-不规则斜导数问题
4. Oblique derivative problem for non-divergence parabolic equations with time-discontinuous coefficients [C] . V. Kozlov, A. Nazarov International Workshop on Advances in Mathematical Analysis of Partial Differential Equations . 2014

机译：具有时间不连续系数的非发散抛物型方程的倾斜衍生问题
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. PARABOLIC SYSTEMS OF DIFFERENTIAL EQUATIONS WITH TIME DEPENDENT COEFFICIENTS [O] . 1957

机译：具有时间相关系数的微分方程的抛物线方程组
7. Oblique derivative problem for non-divergence parabolic equations with discontinuous in time coefficients [O] . Kozlov, Vladimir, Nazarov, Alexander I. 2013

机译：具有时滞的非发散抛物方程的斜导数问题时间系数不连续

Oblique derivative problem for non-divergence parabolic equations with time-discontinuous coefficients

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