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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

3 votes
Accepted

Must $q$ be analytic?

No. $F$ does not put enough constraints on $q$. Suppose that $F$ is a given analytic function, and let $q_0:[0, 1]\to \mathbb R_+$ be continuous. Extend $q_0$ to a function on $\mathbb R_+$ using the …
jarauh's user avatar
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1 vote
Accepted

Empty interior lack of minima

I'm always afraid of confusing lsc and usc, but what about $d=1$ and $U=\mathbb R\setminus\mathbb Q$ and $f(0)=0$ and $f(x) =1$ for $x\neq 0$?
jarauh's user avatar
  • 328