Recovering a variable exponent

Abstract

We consider an inverse problem of recovering the non-linearity in the one dimensional variable exponent $p(x)$-Laplace equation from the Dirichlet-to-Neumann map. The variable exponent can be recovered up to the natural obstruction of rearrangements. The main technique is using a M\"untz-Sz\'asz theorem after reducing the problem to determining a function from its $L^p$-norms.