The field of explainability in machine learning has become very prolific and numerous explanation methods have emerged during the last decade. Local explanations are of major interest because they are intelligible and claim to be locally faithful to the machine learning model. However, there is no guarantee that these explanations can apply to new similar observations. This raises questions about the usefulness of acquired knowledge through such explanations. In this paper, we propose a new concept, which we call the validity domain of explanations. This consists in searching for a region around a given local explanation allowing users to determine the extent to which the explanation generalizes. We experimentally show that our approach is more precise regarding the machine learning model and has a better coverage of the dataset than Anchors, a known competitor that paved the way for this issue.