REGULARITY OF HESSIAN FOR NONDIVERGENCE PARABOLIC AND ELLIPTIC EQUATIONS WITH MEASURABLE COEFFICIENTS

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REGULARITY OF HESSIAN FOR NONDIVERGENCE PARABOLIC AND ELLIPTIC EQUATIONS WITH MEASURABLE COEFFICIENTS

机译：Hessian对于具有可测量系数的抛物线抛物线和椭圆方程的规律性

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We prove the interior L-p(.)-estimates for the Hessian of strong solutions to nondivergence parabolic equations u(t)(x, t) - a(ij)(x, t)D(ij)u(x, t) = f(x, t) and elliptic equations a(ij)(x)D(ij)u(x) = f(x), respectively. Besides a natural assumption that p(.) is log-Holder continuous, we also assume that the coefficients a(ij)(x, t) and a(ij)(x) are merely measurable in one of spatial variables and have small BMO semi-norms with respect to other variables.

机译：我们证明了内部LP（。） - 对Hessian的强大解决方案的估计到不道而口抛物线方程U（t）（x，t） - a（x，t）d（x，t）= F（x，t）和椭圆方程A（ij）（x）d（ij）u（x）= f（x）。除了P（。）是记录器连续的自然假设之外，我们还假设系数a（ij）（x，t）和a（ij）（x）仅在空间变量之一中可测量并且具有小的BMO 关于其他变量的半规范。

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《Communications on pure and applied analysis》 |2020年第5期|共20页
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正文语种 eng
中图分类数学;
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Nondivergence parabolic equations; nondivergence elliptic equations; variable exponent Lebesgue spaces; partially BMO; log-Holder continuity;

机译：不足抛物线方程;不接触椭圆方程;可变指数的lebesgue空间;部分BMO;记录器连续性;

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1. REGULARITY OF HESSIAN FOR NONDIVERGENCE PARABOLIC AND ELLIPTIC EQUATIONS WITH MEASURABLE COEFFICIENTS [J] . Communications on pure and applied analysis . 2020,第5期

机译：Hessian对于具有可测量系数的抛物线抛物线和椭圆方程的规律性
2. Regularity in generalized Morrey spaces of solutions to higher order nondivergence elliptic equations with VMO coefficients [J] . Gadjiev Tahir, Galandarova Shahla, Guliyev Vagif Electronic Journal of Qualitative Theory of Differential Equations . 2019,第55期

机译：具有VMO系数的高阶不发散椭圆型方程解的广义Morrey空间的正则性。
3. W^{2,p(cdot )}-regularity for elliptic equations in nondivergence form with BMO coefficients [J] . Sun-Sig Byun, Mikyoung Lee, Jihoon Ok Mathematische Annalen . 2015,第3a4期

机译：具有BMO系数的非散度形式的椭圆型方程的W ^ {2，p（cdot）}-正则性
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. Linear Parabolic Differential Equations of Arbitrary Order; General Boundary-Value Problems for Elliptic Equations [O] . Felix E. Browder 1953

机译：任意阶线性抛物线方程椭圆方程的一般边值问题
7. A weighted Sobolev regularity theory of the parabolic equations with measurable coefficients on conic domains in Rd [O] . Kyeong-Hun Kim, Kijung Lee, Jinsol Seo 2021

机译：抛物面方程的加权SOBOLEV规律性理论，具有可衡量系数在RD中的圆形域
8. Local Behaviour of Solutions of Degenerate Parabolic Equations with Measurable Coefficients [R] . DiBenedetto, E. 1984

机译：具有可测系数的退化抛物方程解的局部行为

REGULARITY OF HESSIAN FOR NONDIVERGENCE PARABOLIC AND ELLIPTIC EQUATIONS WITH MEASURABLE COEFFICIENTS

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