论文标题
本地Hölder和具有超季度术语的椭圆方程解的最大规律性
Local Hölder and maximal regularity of solutions of elliptic equations with superquadratic gradient terms
论文作者
论文摘要
我们研究了当地的Hölder规律性强溶液的$ U $二阶椭圆方程，具有梯度术语，具有超二次增长$γ> 2 $，在Lebesgue Space $ l^Q $中右侧。当$ q> n \ frac {γ-1}γ$（$ n $是欧几里得空间的维度）时，我们获得了最佳的Hölder连续性指数$α_Q> \ frac {γ-2} {γ-1} $。这使我们能够证明最大规律性类型的一些新结果，这些结果包括估计$ u $ $ u $ in $ l^q $的Hessian矩阵。我们的方法基于爆破技术和liouville定理。
We study the local Hölder regularity of strong solutions $u$ of second-order uniformly elliptic equations having a gradient term with superquadratic growth $γ> 2$, and right-hand side in a Lebesgue space $L^q$. When $q > N\frac{γ-1}γ$ ($N$ is the dimension of the Euclidean space), we obtain the optimal Hölder continuity exponent $α_q > \frac{γ-2}{γ-1}$. This allows us to prove some new results of maximal regularity type, which consist in estimating the Hessian matrix of $u$ in $L^q$. Our methods are based on blow-up techniques and a Liouville theorem.
