We study regularity properties of solutions to elliptic equations by uncovering geometric structures implicitly encoded in the equations themselves. Rather than arising from explicit constraints or physical interfaces, these structures emerge through degeneracies, weights, or abrupt changes in the equation. We interpret them as abstract or “non-physical” free boundaries. These hidden features play a decisive role in governing the local behavior of solutions and conceal intrinsic regularizing mechanisms. By analyzing them within a free boundary framework, we obtain higher-order regularity results in regions where the behavior of the solution is a priori unclear.