具有混合边界条件的笛卡儿积上的拉普拉斯算子
The Laplacian on Cartesian products with mixed boundary conditions
摘要：
利用二次型定义了具有混合边界条件的笛卡儿积上的拉普拉斯算子。证明了它与齐次和某些混合边界条件的标准定义的一致性，并由此导出了相应的一阶索伯列夫空间的张量表示.证明了该区域属于二阶索伯列夫空间的一个判别准则。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
