Higher regularity estimates for solutions to $\mathrm{\infty }$-Laplacian-type models

In this work, we tackle the higher regularity estimates of solutions to inhomogeneous $\mathrm{\infty }-$Laplacian equations at interior critical points. Our estimates provide smoothness properties better than the corresponding available regularity for the model with bounded forcing terms. We explore several scenarios, thereby obtaining improved regularity estimates, which depend on the universal parameters of the model. Our findings connect with nowadays well-known estimates developed for obstacle and dead-core type problems.