论文标题
一般域中高阶操作员的最大原理
Maximum Principle for Higher Order Operators in General Domains
论文作者
论文摘要
我们首先证明了$ w^{1，t}（ω）$，$ω\ subset \ mathbb {r}^n $中的功能的功能的de giorgi类型级别估计值，带有$ t> n \ geq 2 $。这种增强的集成性使我们能够为功能建立新的Harnack类型不平等，而不一定属于De Giorgi的类别，如[Di Benedetto-trudinger，AIHP（1984）]在$ W^{1,2} $中的功能中所获得的。结果，我们证明了在第二和第三的相当通用的域中，在相当通用的域中，强大的最大原理对均匀的椭圆运算符的有效性，只要考虑了二阶导数。
We first prove De Giorgi type level estimates for functions in $W^{1,t}(Ω)$, $Ω\subset\mathbb{R}^N$, with $t>N\geq 2$. This augmented integrability enables us to establish a new Harnack type inequality for functions which do not necessarily belong to De Giorgi's classes as obtained in [Di Benedetto--Trudinger, AIHP (1984)] for functions in $W^{1,2}$. As a consequence, we prove the validity of the strong maximum principle for uniformly elliptic operators of any even order, in fairly general domains in dimension two and three, provided second order derivatives are taken into account.
