We establish a new approach of treating elliptic boundary value problems (BVPs) on manifolds with boundary and regular corners, up to singularity order 2. Ellipticity and parametrices are obtained in terms of symbols taking values in algebras of BVPs on manifolds of corresponding lower singularity orders. Those refer to Boutet de Monvel’s calculus of operators with the transmission property, see Boutet de Monvel (Acta Math 126:11–51, 1971) for the case of smooth boundary. On corner configuration operators act in spaces with multiple weights. We mainly study the case of upper left entries in the respective \(2\times 2\) operator block-matrices of such a calculus. Green operators in the sense of Boutet de Monvel (Acta Math 126:11–51, 1971) analogously appear in singular cases, and they are complemented by contributions of Mellin type. We formulate a result on ellipticity and the Fredholm property in weighted corner spaces, with parametrices of analogous kind.

我们建立了一种新的方法来处理具有边界和正角的流形上的椭圆形边值问题（BVP），直到奇异阶数为2。椭圆和参量是通过在相应的较低奇异阶上的BVPs代数中的值取符号的方式获得的。这些指的是具有传输性质的Boutet de Monvel算子的演算，有关光滑边界的情况，请参见Boutet de Monvel（Acta Math 126：11-51，1971）。在角落配置中，运算符在具有多个权重的空间中起作用。我们主要研究各个\（2 \ times 2 \）中左上角条目的情况这种微积分的算子块矩阵。Boutet de Monvel意义上的绿色算符（Acta Math 126：11–51，1971）类似地出现在单个情况下，并且得到梅林类型的补充。我们用类似种类的参数，对加权角空间中的椭圆率和Fredholm性质制定了一个结果。