论文标题
部分可观测时空混沌系统的无模型预测
Sobolev spaces on arbitrary domains and semigroups generated by fractional Laplacian
论文作者
论文摘要
我们描述了一个程序，以引入Sobolev空间和分数Dirichlet Laplacian生成的半群，上面是$ \ r^d $的任意域。特别是，将讨论非殖民和均匀类型的空间以及其双重性能，嵌入和Gagliardo-Nirenberg的不平等的明确定义。我们还显示了半群的连续性和平滑属性。
We describe a procedure to introduce Sobolev spaces and the semigroup generated by the fractional Dirichlet Laplacian on an arbitrary domain of $\R^d$. In particular, the well-definedness of the spaces of both non-homogeneous and homogeneous type together with their duality properties, embeddings, and Gagliardo-Nirenberg inequalities will be discussed. We also show the continuity and the smoothing property of the semigroup.
