List questions from calculus-of-variations

Published on 23 Mar 2026 - 0:29

100

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$T$ and $x_T-x_0$? no extremals of $J[x]= \int_0^T \frac{m}{2} \dot x^2 - \frac{k}{2}x^2 dt$ in $S=\{x \in C^1([0,T]): x(0)=x_0,x(T)=x_T\}$

Published on 25 Mar 2026 - 11:11

56

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Find optimal x(t) such that L(t) = R(x(t)) as close as possible.

Published on 25 Mar 2026 - 15:58

121

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The chain rule for functionals

Published on 24 Mar 2026 - 17:32

130

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Analog of du Bois-Reymond for when h is in another function

Published on 25 Mar 2026 - 0:43

40

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Confusion about Theorem 5.5 in Struwe's book

Published on 25 Mar 2026 - 14:39

112

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Equation of motion with respect to the metric.

Published on 25 Mar 2026 - 3:03

86

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Step in the motivation of Lax-Milgram with membrane problem.

Published on 25 Mar 2026 - 7:01

81

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Find extremum of functional $\int\limits_{x_0}^{x_1}{1+y^2\over \dot{y}^2}$

Published on 25 Mar 2026 - 6:12

205

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Minimizing sequence for a quadratic energy functional is Cauchy

Published on 24 Mar 2026 - 21:41

265

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Euler -Lagrange equation: variational Problem min $K[u]$ for $K[u]=\int_D(|\nabla u|^2+\frac{1}{2}gu^4)dxdy$

Published on 25 Mar 2026 - 6:12

356

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Method of Lagrange multipliers for constrained minimum of functional

Published on 25 Mar 2026 - 10:28

1.7k

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Minimization of functional using Euler-Lagrange

Published on 25 Mar 2026 - 6:09

68

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Integral equation to determine curve shapes

Published on 25 Mar 2026 - 14:09

93

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Minimiser of perturbed functional and Laplace's equation

Published on 25 Mar 2026 - 11:30

List Question

Geometric Calculus, Clifford Algebra, and Calculus of Variations

$T$ and $x_T-x_0$? no extremals of $J[x]= \int_0^T \frac{m}{2} \dot x^2 - \frac{k}{2}x^2 dt$ in $S=\{x \in C^1([0,T]): x(0)=x_0,x(T)=x_T\}$

Find optimal x(t) such that L(t) = R(x(t)) as close as possible.

The chain rule for functionals

Analog of du Bois-Reymond for when h is in another function

Confusion about Theorem 5.5 in Struwe's book

Equation of motion with respect to the metric.

Step in the motivation of Lax-Milgram with membrane problem.

Find extremum of functional $\int\limits_{x_0}^{x_1}{1+y^2\over \dot{y}^2}$

Minimizing sequence for a quadratic energy functional is Cauchy

Euler -Lagrange equation: variational Problem min $K[u]$ for $K[u]=\int_D(|\nabla u|^2+\frac{1}{2}gu^4)dxdy$

Method of Lagrange multipliers for constrained minimum of functional

Minimization of functional using Euler-Lagrange

Integral equation to determine curve shapes

Minimiser of perturbed functional and Laplace's equation

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