论文标题
带有欧几里得切线的度量空间中的Bourgain-Brezis-Mironescu方法
Bourgain-Brezis-Mironescu approach in metric spaces with Euclidean tangents
论文作者
论文摘要
在设置度量尺寸的设置中，满足双重状况以及$（1，p）$-Poincaré的不平等现象，我们证明了Bourgain-Brezis-Mironescu在Sobolev Space $ W^{1，P}（x，d，d，d，d，ν）$中的$ $ $ $ $的指标类似物。指向Gromov-Hausdorff Sense中的切线空间是欧几里得，固定尺寸$ n $。
In the setting of metric measure spaces satisfying the doubling condition and the $(1,p)$-Poincaré inequality, we prove a metric analogue of the Bourgain-Brezis-Mironescu formula for functions in the Sobolev space $W^{1,p}(X,d,ν)$, under the assumption that for $ν$-a.e. point the tangent space in the Gromov-Hausdorff sense is Euclidean with fixed dimension $N$.
