论文标题
具有第一阶或二阶电位的一般线性约束的Müller-Zhang截断
Müller-Zhang truncation for general linear constraints with first or second order potential
论文作者
论文摘要
令$ \ mathcal {b} $为订单$ l = 1 $或$ l = 2 $的同质差分运算符。我们表明，表格$（\ Mathcal {b} u_j）_j $在$ l^1 $ sense中融合到紧凑型，convex set $ k $可以均匀地将序列融合到此设置的序列中，只要订单$ l $均匀地界限。我们在整个空间，一个开放式域中证明了我们的结果版本，并且在$ k $上均连续地在一个开放的有限域上连续变化。这是S.Müller对梯度序列证明的定理的有条件概括。 [6]。此外，构建了线性化的等递质欧拉系统的两阶潜力。
Let $\mathcal{B}$ be a homogeneous differential operator of order $l=1$ or $l=2$. We show that a sequence of functions of the form $(\mathcal{B}u_j)_j$ converging in the $L^1$-sense to a compact, convex set $K$ can be modified into a sequence converging uniformly to this set provided that the derivatives of order $l$ are uniformly bounded. We prove versions of our result on the whole space, an open domain, and for $K$ varying uniformly continuously on an open, bounded domain. This is a conditional generalization of a theorem proved by S. Müller for sequences of gradients, cf. [6]. Moreover, a potential of order two for the linearized isentropic Euler system is constructed.
