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What is the connection between calculus of variations and PDEs?

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#partial-differential-equations #calculus-of-variations
352
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A property of area functional

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#differential-geometry #calculus-of-variations #geometric-measure-theory #minimal-surfaces
432
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Evans Chap 8.12 - Constant Mean Curvature Surface and Variations

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#partial-differential-equations #calculus-of-variations
43
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Functional derivative of the function $\phi(y,y',x)$ w.r.t. $y$

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#calculus-of-variations
179
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Optimal way to cut grass on the rectangular area.

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#optimization #euclidean-geometry #calculus-of-variations
1.1k
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Weak convergence in $L^1$ of a tight sequence

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#functional-analysis #calculus-of-variations #weak-convergence
878
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Variation of the derivative

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#multivariable-calculus #calculus-of-variations
664
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Evans 8.13: Dual Variational Principle

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#partial-differential-equations #convex-analysis #calculus-of-variations
144
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Understanding the Lemma 2 of Calculus of Variations

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#calculus #calculus-of-variations #euler-lagrange-equation
663
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Calculus of Variation: Trouble finding the Euler-Lagrange equation

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#matrices #ordinary-differential-equations #normed-spaces #calculus-of-variations #euler-lagrange-equation
6.2k
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How to minimize the integral of the functional of a function, with respect to that function?

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#calculus #derivatives #calculus-of-variations #maxima-minima
76
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What Jordan curve of length $1$ maximizes the expected length of a chord between two uniformly picked points on it?

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#probability #differential-geometry #calculus-of-variations #plane-geometry
346
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All the symmetries of the Dirichlet energy are conformal

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#reference-request #riemannian-geometry #calculus-of-variations #symmetry #variational-analysis
169
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Is there a way to write the variation of a functional in terms of the shift operator

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#taylor-expansion #calculus-of-variations #maxima-minima
302
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Fundamental Lemma for variational calculus for measurable function

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#functional-analysis #calculus-of-variations

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