For \(p \in (1, \infty )\) and \(s \in (0,1)\) , we consider the following mixed local-nonlocal equation P \(\begin{aligned} - \Delta _p u + (-\Delta _p)^s u = f \; \text {in} \; \Omega , \end{aligned}\) where \(\Omega \subset \mathbb {R}^d\) is a bounded domain and the function \(f \in L_{loc}^1(\Omega )\) . Depending on the dimension d, we prove gradient potential estimates of weak solutions to (P) for the entire ranges of p and s. As a byproduct, we recover the corresponding estimates in the purely diffusive setup, providing connections between the local and nonlocal aspects of the equation. Our results are new, even for the linear case \(p=2\) .
