feat(Analysis/Calculus/FDeriv): continuous differentiability from continuous partial derivatives on an open domain in a product space#25304
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…nditions for continuous differentiability from continuous partial derivatives.
PR summary bd82942c80Import changes for modified filesNo significant changes to the import graph Import changes for all files
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Thank you for the PR! Here are a few preliminary comments.
Co-authored-by: grunweg <rothgami@math.hu-berlin.de>
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…nearEquiv.prodComm (leanprover-community#25564) `ContinuousLinearMap.coprod_comp_prodComm` shows that pre-composition of a coproduct with prodComm swaps the terms in the coproduct. A dependency of leanprover-community#25304. Co-authored-by: igorkhavkine <133780155+igorkhavkine@users.noreply.github.com>
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…nearEquiv.prodComm (leanprover-community#25564) `ContinuousLinearMap.coprod_comp_prodComm` shows that pre-composition of a coproduct with prodComm swaps the terms in the coproduct. A dependency of leanprover-community#25304. Co-authored-by: igorkhavkine <133780155+igorkhavkine@users.noreply.github.com>
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…nearEquiv.prodComm (leanprover-community#25564) `ContinuousLinearMap.coprod_comp_prodComm` shows that pre-composition of a coproduct with prodComm swaps the terms in the coproduct. A dependency of leanprover-community#25304. Co-authored-by: igorkhavkine <133780155+igorkhavkine@users.noreply.github.com>
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If a function
f : E × F → Gis continuously differentiable, then its partial derivatives alongEandFare also continuous. The non-trivial converse implication holds when the partial derivatives are continuous on an open domain, and they can be added together to give the total derivative off. See this #mathlib4 > Partial derivatives @ 💬 and the containing thread for some discussion. The PR creates a new import (Mathlib.Analysis.Calculus.FDeriv.Partial), where other results about partial derivatives could go in the future.