We prove a disc formula for the weighted Siciak-Zahariuta extremal function for an upper semicontinuous function q on an open connected subset X in ℂⁿ. This function is also known as the weighted Green function with logarithmic pole at infinity and weighted global extremal function.
We establish plurisubharmonicity of envelopes of certain classical disc functionals on locally irreducible complex spaces, thereby generalizing the corresponding results for complex manifolds. We also find new formulae expressing the Siciak-Zaharyuta extremal function of an open set in a locally irreducible affine algebraic variety as the envelope of certain disc functionals, similarly to what has been done for open sets in ℂⁿ by Lempert and by Lárusson and Sigurdsson.