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Results tagged with laplacian
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user 129213
The Laplacian matrix is the representation of a graph in matrix form.
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Embedding of domain of fractional power of Laplacian into Sobolev space for cylindrical domains
On a bounded domain $\Omega \subset \mathbb R^d, d\geq 2$ with smooth boundary, it is well known that for the Dirichlet Laplacian $\Delta_D$, $D((-\Delta_D)^\frac12) = H^1_0(\Omega)$. … I found a reference [1] which asserts that in this case, the Dirichlet Laplacian satisfies the maximal $L^p$-regularity property and fractional powers of $-\Delta_D$ are well-defined. …
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