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Is $f^{-a}$ locally integrable if $f\geq 0$ has a unique stationary point ( a minimum) at wh...

Let $0<a<d/2$, let $B$ be the unit ball in $\mathbb{R}^{d}$ centered at the origin, and let $f:B \to [0,\infty[$ be a a smooth function such that (1) $f(x)\geq f(0).$ (2) $\nabla f(x)\neq 0,\quad \for …