论文标题
定量runge类型近似定理，用于某些部分差分运算符的零解决方案
Quantitative Runge type approximation theorems for zero solutions of certain partial differential operators
论文作者
论文摘要
我们证明了具有恒定系数的几类线性部分差分运算符的平滑零解的空间的定量runge类型近似结果。除其他外，我们还将在一个空间变量中为凸组，椭圆运算符，抛物线运算符和波浪运算符的任意操作员建立此类结果。我们的方法的灵感来自对部分差分运算符内核的线性拓扑不变性的研究。作为我们工作的一部分，我们还为子空间椭圆操作员展示了定性runge型近似定理，这似乎是新的并且具有独立的兴趣。
We prove quantitative Runge type approximation results for spaces of smooth zero solutions of several classes of linear partial differential operators with constant coefficients. Among others, we establish such results for arbitrary operators on convex sets, elliptic operators, parabolic operators, and the wave operator in one spatial variable. Our methods are inspired by the study of linear topological invariants for kernels of partial differential operators. As a part of our work, we also show a qualitative Runge type approximation theorem for subspace elliptic operators, which seems to be new and of independent interest.
