integration_by_parts
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| integration_by_parts [2023/06/08 08:20] – spencer | integration_by_parts [2023/06/08 08:21] (current) – [Integration by Parts II (the formal adjoint of the exterior derivative)] spencer | ||
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| $$(d\alpha, \beta) = (\alpha, \delta \beta) + \int_{\partial M} \langle \alpha, \iota_{\nu} \beta\rangle \mathrm{vol}_{\partial M}.$$ | $$(d\alpha, \beta) = (\alpha, \delta \beta) + \int_{\partial M} \langle \alpha, \iota_{\nu} \beta\rangle \mathrm{vol}_{\partial M}.$$ | ||
| Probably. Would have to check whether boundary terms arise in the first step where we move $e(\omega^i)$ to the other side too. | Probably. Would have to check whether boundary terms arise in the first step where we move $e(\omega^i)$ to the other side too. | ||
| + | Certainly in the compactly supported case $(d\alpha, | ||
| + | Of course, we also have $\delta = d^* = (-1)^{|\alpha| + 1} \star^{-1} d \star$ for $\star$ the Hodge star operator. | ||
integration_by_parts.1686226840.txt.gz · Last modified: by spencer