论文标题
在气缸域和卡尔曼的配方中近似抛物线层型式操作员的解决方案的近似
Approximation of solutions to parabolic Lamé type operators in cylinder domains and Carleman's formulas for them
论文作者
论文摘要
令$ s \ in {\ mathbb n} $，$ t_1，t_2 \ in {\ mathbb r} $，$ t_1 <t_2 $，以及让$ω$，在$ {\ mathbb r}^n $，$ n \ geq 1 $ $ n \ geq 1 $ coppement $ geq $ propement $ gem和cropt $ω$ω$ω$ω$ω$ω$ω$ω$ω$ω$ω$ω中和the sepsit umm和aptset ymhom和aptset ymm和没有非空的紧凑型组件 $ω$。我们研究了Lebesgue类的解决方案近似于抛物线层型型型系统的问题 $ l^2（ω\ times（t_1，t_2））$在气缸域中 $ω\ times（t_1，t_2）\ subset {\ mathbb r}^{n+1} $通过更大域$ω\ times（t_1，t_2）$中的更多常规解决方案。作为获得的近似定理的应用，我们构建了Carleman的公式，用于从Sobolev类$ h^{2s，s}（ω\ times（T_1，t_2））$通过值的溶液中的解决方案的一部分的溶液和相应的构图。
Let $s \in {\mathbb N}$, $T_1,T_2 \in {\mathbb R}$, $T_1<T_2$, and let $Ω, ω$ be bounded domains in ${\mathbb R}^n$, $n \geq 1$ such that $ω\subset Ω$ and the complement $Ω\setminus ω$ have no non-empty compact components in $Ω$. We investigate the problem of approximation of solutions to parabolic Lamé type system from the Lebesgue class $L^2(ω\times (T_1,T_2))$ in a cylinder domain $ω\times (T_1,T_2) \subset {\mathbb R}^{n+1}$ by more regular solutions in a bigger domain $Ω\times (T_1,T_2)$. As an application of the obtained approximation theorems we construct Carleman's formulas for recovering solutions to these parabolic operators from the Sobolev class $H^{2s,s}(Ω\times (T_1,T_2))$ via values the solutions on a part of the lateral surface of the cylinder and the corresponding them stress tensors.
