Variable exponent Calderón's problem in one dimension

We consider one-dimensional Calderón's problem for the variable exponent p(·)-Laplace equation and find out that more can be seen than in the constant exponent case. The problem is to recover an unknown weight (conductivity) in the weighted p(·)-Laplace equation from Dirichlet and Neumann data of solutions.

We give a constructive and local uniqueness proof for conductivities in L∞ restricted to the coarsest sigma-algebra that makes the exponent p(·) measurable.