# Questions tagged [calculus-of-variations]

Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.

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### Inf sup condition for discrete Stokes problem

I am considering the discrete inf-sup condition for the discrete Stokes problem $\inf_{q \in Q_h} \sup_{v \in V_h} \frac{(q, \nabla \cdot v)}{\| q \| \| \nabla v\|} \geq \beta > 0$ This means ...
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### minimizing weighted length of closed curves

Let $\mathcal{A}$ be the family of closed smooth curves in the right half of the complex plane $\mathbb{C}$ such that any curve in the family must enlose the point $z=1$ and tangent to the $y$-axis at ...
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### Functional approach vs jet approach to Lagrangian field theory

Context: I am a PhD student in theoretical physics with higher-than-average education on differential geometry. I am trying to understand Lagrangian and Hamiltonian field theories and related concepts ...
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### Integral of inverse of a function [closed]

Is it possible to obtain an expression to the integral of the inverse of a function, maybe dependent of its primitive. $\int_{0}^t \frac{1}{f(\tau)} d \tau = g(t) - g(0)$ Above the corresponding ...
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### Prove the equicontinuity of a maximizing sequence

Let $X$ be a compact subset of $\mathbb{R}$ and $c(x_1,x_2,x_3,x_4)$ be a fixed bounded continuous functions on $X^4$. Assume $\mu,\nu$ are probability measures on $X^2$, and $\mu\otimes\nu$ is the ...
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### Area of Disc that Intersects Another under Smooth Flow

The following question can be asked in any $\mathbb{R}^n$ for $n > 1$, but the case of interest is (thankfully) the case $n = 2$. The formulation of the problem with discs isn't actually critical ...
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### Energy functional continuous with respect of time $t$

I am studying a paper of Liu Yacheng which named "On potential wells and applications to semilinear hyperbolic equations and parabolic equations" it considers a nonlinear parabolic equation \begin{...
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### Properties of the topology of sequential convergence $\tau_{seq}$

Let $(X,\tau)$ be a Hausdorff space. Denote by $\tau_{seq}$ the topology on $X$ whose closed sets are the sequentially $\tau$-closed subsets of $X$. I have read that $\tau_{seq}$ has the following ...
### Maximize an $L^p$-functional subject to a set of constraints
Let $(E,\mathcal E,\lambda)$ and $(E',\mathcal E',\lambda')$ be measure spaces $f\in L^2(\lambda)$ $I$ be a finite nonempty set $\varphi_i:E'\to E$ be bijective $(\mathcal E',\mathcal E)$-measurable ...