论文标题
部分可观测时空混沌系统的无模型预测
New regularity estimates for fully nonlinear elliptic equations
论文作者
论文摘要
我们为完全非线性椭圆运算符的粘度超溶液建立了新的定量HESSIAN集成性估计值。作为推论，我们表明，在著名的$ w^{2，\ varepsilon} $的最佳Hessian Hessian Power Entigability $ \ varepsilon = \ varepsilon（λ，λ，λ，n）$中）\ right）^{n-1}} {\ ln n n^4} \ cdot \ left（\fracλλλ\ right）常数。特别是，$ \ left（\fracλλ\ right） ^{n-1} \ varepsilon（λ，λ，n）$ bull，为$ n \ to \ infty $;先前的结果产生了这种数量的快速衰变。上层估计改进了阿姆斯特朗，西尔维斯特尔和智能的估计值：1103.3677
We establish new quantitative Hessian integrability estimates for viscosity supersolutions of fully nonlinear elliptic operators. As a corollary, we show that the optimal Hessian power integrability $\varepsilon = \varepsilon(λ, Λ, n)$ in the celebrated $W^{2, \varepsilon}$-regularity estimate satisfies $$\frac{ \left (1+ \frac{2}{3}\left(1- \fracλΛ \right )\right )^{n-1}}{\ln n^4} \cdot \left( \fracλΛ \right) ^{n-1} \le \varepsilon \le \frac{nλ}{(n-1)Λ+λ}, $$ where $n\ge 3$ is the dimension and $0< λ< Λ$ are the ellipticity constants. In particular, $\left( \fracΛλ \right) ^{n-1} \varepsilon(λ, Λ, n)$ blows-up, as $n\to\infty$; previous results yielded fast decay of such a quantity. The upper estimate improves the one obtained by Armstrong, Silvestre, and Smart in arXiv:1103.3677
