Question

Is it possible for a function $f:\mathbb R\to\mathbb R$ to be differentiable in each direction, but not Gâteaux/Fréchet differentiable?

score 66 · Answer 1 · 2026-03-25 15:17:50

66

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Is it possible for a function $f:\mathbb R\to\mathbb R$ to be differentiable in each direction, but not Gâteaux/Fréchet differentiable?

Published on 25 Mar 2026 - 15:17

score 339 · Answer 2 · 2019-08-14 13:13:41

339

Views

Fréchet Derivative of Inner Product

Published on 14 Aug 2019 - 13:13

score 308 · Answer 3 · 2019-08-30 12:05:00

308

Views

Fréchet differentiable operator passing through origin and positive homogenous is linear?

Published on 30 Aug 2019 - 12:05

score 184 · Answer 4 · 2019-08-30 17:46:35

184

Views

Fréchet derivative of non-coercive energy functional $\frac{1}{2}\int_\Omega |\nabla u|^2 - \frac{1}{p}\int_\Omega |u|^p$

Published on 30 Aug 2019 - 17:46

score 68 · Answer 5 · 2019-09-03 07:07:12

68

Views

gateaux derivative of a bilinear map

Published on 03 Sep 2019 - 7:07

score 64 · Answer 6 · 2026-02-24 12:00:32

64

Views

Fréchet-derivative of integral over 1/p |u|^p

Published on 24 Feb 2026 - 12:00

score 290 · Answer 7 · 2026-03-25 15:17:50

290

Views

Generalisation of characterisation of continuous Fréchet-differentiability to infinite dimensions

Published on 25 Mar 2026 - 15:17

score 340 · Answer 8 · 2019-09-24 22:43:43

340

Views

The Frechet Derivative of the usual Functional $\int_a^b F(t,y,y')dt$ in Calculus of Variations

Published on 24 Sep 2019 - 22:43

score 44 · Answer 9 · 2019-09-25 10:11:02

44

Views

Multivariate Function's Differentiability?

Published on 25 Sep 2019 - 10:11

score 69 · Answer 10 · 2019-10-17 06:32:31

69

Views

Cauchy Local Existence and Uniqueness using Implicit Function Theorem for Banach Spaces

Published on 17 Oct 2019 - 6:32

score 59 · Answer 11 · 2026-03-25 09:26:59

59

Views

Fréchet derivative of Ridge regression

Published on 25 Mar 2026 - 9:26

score 669 · Answer 12 · 2019-10-31 16:08:37

669

Views

A continuously differentiable function $f$ Satisfying $ \| f ( x ) - f ( y ) \| \geq \| x - y \| , \forall x , y \in \mathbb { R } ^ { n } $ is onto

Published on 31 Oct 2019 - 16:08

score 28 · Answer 13 · 2026-02-23 03:59:16

28

Views

Stationarity of a constrained local extremum

Published on 23 Feb 2026 - 3:59

score 94 · Answer 14 · 2019-11-01 19:44:30

94

Views

Why does the adjoint of a Fréchet derivative has closed range?

Published on 01 Nov 2019 - 19:44

score 94 · Answer 15 · 2019-11-02 09:47:48

94

Views

Second derivative test in the Hilbert space case

Published on 02 Nov 2019 - 9:47

List Question

Is it possible for a function $f:\mathbb R\to\mathbb R$ to be differentiable in each direction, but not Gâteaux/Fréchet differentiable?

Fréchet Derivative of Inner Product

Fréchet differentiable operator passing through origin and positive homogenous is linear?

Fréchet derivative of non-coercive energy functional $\frac{1}{2}\int_\Omega |\nabla u|^2 - \frac{1}{p}\int_\Omega |u|^p$

gateaux derivative of a bilinear map

Fréchet-derivative of integral over 1/p |u|^p

Generalisation of characterisation of continuous Fréchet-differentiability to infinite dimensions

The Frechet Derivative of the usual Functional $\int_a^b F(t,y,y')dt$ in Calculus of Variations

Multivariate Function's Differentiability?

Cauchy Local Existence and Uniqueness using Implicit Function Theorem for Banach Spaces

Fréchet derivative of Ridge regression

A continuously differentiable function $f$ Satisfying $ \| f ( x ) - f ( y ) \| \geq \| x - y \| , \forall x , y \in \mathbb { R } ^ { n } $ is onto

Stationarity of a constrained local extremum

Why does the adjoint of a Fréchet derivative has closed range?

Second derivative test in the Hilbert space case

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