We introduce the notion of recession operator and develop its applications to regularity theory. In brief, this object allows us to displace the assumptions of the original operator to its recession profile. We examine some properties of the recession function and prove results in Sobolev and Hölder spaces. Because ellipticity is invariant under the recession operator, we use this object to examine properties depending only on ellipticity and the dimension. For instance, we study Escauriaza's exponent for a few examples by relating them with the Laplace operator through the recession function. Given the asymptotic character of this structure, we develop density results, also referred to as weak regularity results. A final section discusses important limitations of the method.