论文标题
具有混合边界条件的笛卡尔产品上的拉普拉斯人
The Laplacian on Cartesian products with mixed boundary conditions
论文作者
论文摘要
提出了使用二次形式的带有混合边界条件的笛卡尔产品上的拉普拉斯人的定义。它与同质和某些混合边界条件的标准定义的一致性已得到证明，因此得出了相应的一阶Sobolev空间的张量表示。此外，证明了域属于二阶Sobolev空间的标准。
A definition of the Laplacian on Cartesian products with mixed boundary conditions using quadratic forms is proposed. Its consistency with the standard definition for homogeneous and certain mixed boundary conditions is proved and, as a consequence, tensor representations of the corresponding Sobolev spaces of first order are derived. Moreover, a criterion for the domain to belong to the Sobolev space of second order is proved.
