Improved regularity for the p-Poisson equation

In this paper we produce new, optimal, regularity results for the solutions to p-Poisson equations. We argue through a delicate approximation method, under a smallness regime for the exponent p, that imports information from a limiting profile driven by the Laplace operator. Our arguments contain a novelty of technical interest, namely a sequential stability result; it connects the solutions to p-Poisson equations with harmonic functions, yielding improved regularity for the former. Our findings relate a smallness regime with improved -estimates in the presence of L ∞-source terms.