Boundary determination of coefficients appearing in a perturbed weighted $p$-Laplace equation

We study an inverse boundary value problem associated with $p$-Laplacian which is further perturbed by a linear second order term, defined on a bounded set $\mathrm{\Omega }$ in ${\mathbb{R}}^n,n\ge 2$. We recover the coefficients at the boundary from the boundary measurements which are given by the Dirichlet to Neumann map. Our approach relies on the appropriate asymptotic expansion of the solution and it allows one to recover the coefficients pointwise. Furthermore, by considering the localized Dirichlet-to-Neumann map around a boundary point, we provide a procedure to reconstruct the normal derivative of the coefficients at that boundary point.