Abstract: It is well-known that Lipschitz functions are dense (in energy) in the Newton-Sobolev space defined over an arbitrary metric measure space (with no doubling or Poincaré assumptions). I will present a new proof of this result. The argument covers the case of Newton-Sobolev spaces of exponent $1<p<\infty$, defined over a complete separable metric space endowed with a locally-finite Borel measure. The new approach I will present relies entirely on a smooth analysis: the main tools are some classical theorems in convex analysis and Smirnov's superposition principle for (Euclidean) normal 1-currents.
Based on a joint work with Danka Lučić.
