论文标题
在Lebesgue类$ l^2 $的热量方程的解决方案近似中，更多的常规解决方案
On approximation of solutions to the heat equation from Lebesgue class $L^2$ by more regular solutions
论文作者
论文摘要
令$ s \ in {\ mathbb n} $，$ t_1，t_2 \ in {\ mathbb r} $，$ t_1 <t_2 $和$ω$，在$ {\ mathbb r}^n $，$ n \ egeq 1 $中，$ n \ geq $ geq $ gem，$ geq $ gem，ymm Mathbb r} $ $ω$中的无（非空）组件。我们证明，这是空间的必要条件，$ h^{2s，s} _ {\ Mathcal H}（ω\ times（t_1，t_2））$ of热运算符$ {\ Mathcal h} $ cylinder $ {\ Mathcal H} $ cylinder $ {\ Mathcal H} $ $ h^{2s，s}（ω\ times（t_1，t_2））$要在空间中致密$ l^{2} _ {\ Mathcal H}（ω\ times（ω\ times（t_1，t_2））$，由域$ω\ time（t_1，t_1，t_1，t_1，t_1，t_1，t_1，t_1，t_2））$组成（ω\ times（T_1，T_2））$。作为重要的推论，我们获得了有关Hilbert Space $ H^{2S，S} _ {\ Mathcal H}（ω\ times（ω\ times（t_1，t_2））$ h^{2s，s} _ {2s，t_2））$ h^{2s，s} $ h^{2s，s} $ h^{2s，and $ l^{2} _ {2} _ {tipe（
Let $s \in {\mathbb N}$, $T_1,T_2 \in {\mathbb R}$, $T_1<T_2$, and $Ω, ω$ be bounded domains in ${\mathbb R}^n$, $n \geq 1$, such that $ω\subset Ω$ and the complement $Ω\setminus ω$ has no (non-empty) compact components in $Ω$. We prove that this is the necessary and sufficient condition for the space $H^{2s,s} _{\mathcal H} (Ω\times (T_1,T_2))$ of solutions to the heat operator ${\mathcal H} $ in a cylinder domain $Ω\times (T_1,T_2)$ from the anisotropic Sobolev space $H^{2s,s} (Ω\times (T_1,T_2))$ to be dense in the space $L^{2} _{\mathcal H}(ω\times (T_1,T_2))$, consisting of solutions in the domain $ω\times (T_1,T_2)$ from the Lebesgue class $L^{2} (ω\times (T_1,T_2))$. As an important corollary we obtain the theorem on the existence of a basis with the double orthogonality property for the pair of the Hilbert spaces $H^{2s,s} _{\mathcal H} (Ω\times (T_1,T_2))$ and $L^{2} _{\mathcal H}(ω\times (T_1,T_2))$ .
