论文标题
具有一般性汉密尔顿术语和无界成分的完全非线性椭圆PDE的规律性估计
Regularity estimates for fully nonlinear elliptic PDEs with general Hamiltonian terms and unbounded ingredients
论文作者
论文摘要
我们开发了一种最佳的规律性理论，该理论以非散发形式的完全非线性椭圆形方程的$ l^p $ viscosity解决方案开发，其梯度的生长是通过可测量且可能无界系数的哈密顿功能来描述的。我们的方法以统一的方式对待超级线性和均匀的梯度制度。 我们显示$ c^{0，α} $，$ c^{0，\ textrm {log-lip}} $，$ c^{1，α} $，$ c^{1，\ textrm {log-lip}}} $和$ c^{2，2，α} $ nlinian允许的增长，并订购Hamilton，并订购Hamilton，系数，当我们接近二次制度时，其可集成性又会变得更糟。 此外，我们发现适当的兼容性条件在这些条件下，我们的规律性结果本质上取决于基本源项的整合性。作为我们方法的副产品，我们证明了BMO的先验估计。在放松的凸度假设下，对相关的衰退和扁平轮廓的急剧规律性；改善了一类单数PDE的规律性；以及在无界成分下产生的perron类型。
We develop an optimal regularity theory for $L^p$-viscosity solutions of fully nonlinear uniformly elliptic equations in nondivergence form whose gradient growth is described through a Hamiltonian function with measurable and possibly unbounded coefficients. Our approach treats both superlinear and sublinear gradient regimes in a unified way. We show $C^{0,α}$, $C^{0,\textrm{Log-Lip}}$, $C^{1,α}$, $ C^{1,\textrm{Log-Lip}}$ and $C^{2,α}$ regularity estimates, by displaying the growth allowed to the Hamiltonian in order to deal with an unbounded nonlinear gradient coefficient, whose integrability in turn gets worse as we approach the quadratic regime. Moreover, we find proper compatibility conditions for which our regularity results depend intrinsically on the integrability of the underlying source term. As a byproduct of our methods, we prove a priori BMO estimates; sharp regularity to associated recession and flat profiles under relaxed convexity assumptions; improved regularity for a class of singular PDEs; and a Perron type result under unbounded ingredients.
