  We want to reconstruct a signal based on inhomogeneous data (the amount of
data can vary strongly), using the model of regression with a random design.
Our aim is to understand the consequences of inhomogeneity on the accuracy of
estimation within the minimax framework. Using the uniform metric weighted by a
spatially-dependent rate as a benchmark for an estimator accuracy, we are able
to capture the deformation of the usual minimax rate in situations with local
lacks of data (modelled by a design density with vanishing points). In
particular, we construct an estimator both design and smoothness adaptive, and
a new criterion is developed to prove the optimality of these deformed rates.
