We prove that for elliptic and canceling linear partial differential operators \({\mathbb {B}}\) of order n on \({\mathbb {R}}^n\), continuity of a map u can be inferred from the fact that \({\mathbb {B}}u\) is a measure. We also prove strict continuity of the embedding of the space \({\text {BV}}^{\mathbb {B}}({\mathbb {R}}^n)\) into the space of continuous functions vanishing at infinity. Here, \({\text {BV}}^{\mathbb {B}}(\varOmega )\) denotes the space of vector fields \(u\in {\text {W}}^{n-1,1}(\varOmega )\) such that \({\mathbb {B}}u\) is a finite vectorial measure on the open set \(\varOmega \subset {\mathbb {R}}^n\). For cubes \(Q\subset {\mathbb {R}}^n\), the class of operators \({\mathbb {B}}\) such that \({\text {BV}}^{\mathbb {B}}(Q)\subset {\text {C}}({\bar{Q}})\) is also characterized.

我们证明，对于\（{\ mathbb {R}} ^ n \）上阶为n的椭圆和抵消线性偏微分算子\ {{\ mathbb {B}} \ }，可以从映射u推断出映射u的连续性。\（{\ mathbb {B}} u \）是度量的事实。我们还证明了将空间\（{\ text {BV}} ^ {\ mathbb {B}}（{\ mathbb {R}} ^ n）\）嵌入到连续函数在无穷大时消失的严格连续性。在这里，\（{\ text {BV}} ^ {\ mathbb {B}}（\ varOmega）\）表示矢量字段的空间\（u \ in {\ text {W}} ^ {n-1,1 }（\ varOmega）\），使得\（{\ mathbb {B}} u \）是开放集上的有限矢量量度\（\ varOmega \ subset {\ mathbb {R}} ^ n \）。对于多维数据集\（Q \ subset {\ mathbb {R}} ^ n \），运算符类\（{\ mathbb {B}} \）使得\（{\ text {BV}} ^ {\ mathbb { B}}（Q）\ subset {\ text {C}}（{\ bar {Q}}）\）也被表征。