MathOverflow

Let $\Omega$ be an open, bounded, convex subset of $\mathbb R^n$. Given a Lipschitz function $f$ on $\Omega$, we denote by $D(f)$ the subset of $\Omega$ on which the classical derivative of $f$ exists.
Consider the set $\mathcal D$ of Lipschitz functions $f: \Omega \to \mathbb R$ whose derivative is everywhere discontinuous as a function on $D(f)$....

I'm trying to understand the behavior of the Klein-Gordon propagator near a hypersurface where one metric component diverges.Consider a Lorentzian metric of the form:ds² = -A(r)dt² + [A(r)B(ρ)]⁻¹dr² + r²dΩ²where B(ρ) → 0 at a specific hypersurface ρ...

It is well known that there is no general formula for the solution of the quintic. Of course, what this really means is that there is no general formula that only involves addition, subtraction, multiplication, division, and the extraction of $n$-th...

It is well known that given a finite, connected, weighted graph ($G = (V,E,w)$), one can view it as a discrete metric space by defining the induced shortest-path metric[d_G(x,y) = \inf_{\gamma:x\to y} \sum_{e \in \gamma} w(e).]In this setting, the graph...