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Question on a derivative on a Hilbert space

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#analysis #derivatives #hilbert-spaces #gateaux-derivative
52
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Directional derivative of $f:H^1 \to H^1$

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223
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Is my derivation of the Gateaux derivative correct and rigorous?

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#proof-verification #gateaux-derivative
1k
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Frechet and Gateaux derivative of integrals

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#real-analysis #sobolev-spaces #differential #frechet-derivative #gateaux-derivative
798
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Meaning of functional differentiability

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#derivatives #calculus-of-variations #frechet-derivative #gateaux-derivative
92
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Proving/disproving a sufficient condition for Gâteaux differentiability

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#banach-spaces #gateaux-derivative
333
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Failure of chain rule for Gâteaux derivative on an arbitrary Banach space

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#analysis #gateaux-derivative
95
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Counter-example for Gateaux derivative being continuous

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#banach-spaces #frechet-derivative #gateaux-derivative
60
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Why does "t" in the formula for gateaux differentiation represent a scalar value?

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#multivariable-calculus #linear-transformations #gateaux-derivative
1.5k
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An example of Gateaux derivative

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#derivatives #gateaux-derivative
290
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Gâteaux derivate of the Tikhonov functional

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#functional-analysis #derivatives #regularization #gateaux-derivative
290
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Prove Gateaux derivative implies Fréchet derivative in some condition

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#derivatives #frechet-derivative #gateaux-derivative
262
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Citation for the Gateaux derivative FTC

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#calculus-of-variations #gateaux-derivative
1.1k
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Mean value inequality in the framework of Banach spaces.

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#functional-analysis #proof-explanation #banach-spaces #hahn-banach-theorem #gateaux-derivative
149
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Does the Euler-Lagrange functional actually have a functional derivative?

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#calculus-of-variations #euler-lagrange-equation #gateaux-derivative

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