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Denote by $\mathcal L$ the set of continuously differentiable real valued functions on $[0, 1]$ with Lipschitz continuous derivative. Does there exist a Borel measurable function $ f: [0, 1] \times \m …

You are in a plane at some point on Earth. You want to be at the earliest time zone possible at the end of your flight. What is the optimal path to take? Formally, fix spherical coordinates $(\theta, …

This is a close relative of the following problem. Let $\Omega$ be an open, bounded subdomain of $\mathbb R^n$ with smooth boundary, and $f_i \in W^{1, \infty} (\Omega)$ a sequence of functions equibo …

Let $f_i \in L^1 ([0, 1])$ be a sequence of functions equibounded in $L^1$ norm - that is, there exists some $M > 0$ such that $\|f_i\|_{L^1} < M$. Define the functional $F: L^1([0, 1]) \to \mathbb R$ …

1. On the $L^\infty$ calculus of variations: The field known as the $L^\infty$ calculus of variations is a relatively new field that concerns itself with minimising functionals involving the supremum …