论文标题
在跟踪定理上，用于加权混合标准Sobolev空间和应用
On trace Theorems for weighted mixed norm Sobolev spaces and applications
论文作者
论文摘要
我们证明，在上半年空间中，重量是垂直变量的功能函数的加权混合标准Sobolev空间的定理。结果表明，痕量函数的可不同性顺序仅取决于权重功能和相对于垂直变量集成的集成能力，而不取决于集成相对于水平的功能。即使在非加权情况下，它们也是新的，并且在未混合的规范空间的情况下，它们恢复了经典的结果。这项工作是由针对具有各向异性特征且具有非均匀边界条件的椭圆形和抛物线方程解决方案解决方案解决方案的研究的动机。该结果为研究以可测量系数的差异形式研究了分数椭圆形和抛物线方程的研究提供了必不可少的要素。
We prove trace theorems for weighted mixed norm Sobolev spaces in the upper-half space where the weight is a power function of the vertical variable. The results show the differentiability order of the trace functions depends only on the power in the weight function and the integrability power for the integration with respect to the vertical variable but not on the integrability powers for the integration with respect to the horizontal ones. They are new even in the un-weighted case and they recover classical results in the case of un-mixed norm spaces. The work is motivated by the study of regularity theory for solutions of elliptic and parabolic equations with anisotropic features and with non-homogeneous boundary conditions. The results provide an essential ingredient to the study of fractional elliptic and parabolic equations in divergence form with measurable coefficients.
