Understanding the fault behavior through geodetic data has an important impact in our assessment of the seismic hazard. To shed light on the aseismic evolution of a fault, we developed a new slip inversion strategy, the ELADIN (ELastostatic ADjoint INversion) method, that uses the adjoint elastostatic equations to efficiently compute the gradient of the cost function. ELADIN is a 2-steps inversion algorithm to better handle the slip constraints. In the first step, it finds the slip that better explain the data without any constraints and the second step refines the solution imposing the slip constraints through a Gradient Projection Method. In order to get a physical plausible slip distribution and to overcome the poor fault illumination due to scarce data, ELADIN reduces the solution space by means of a von Karman autocorrelation function that controls the wavenumber content of the solution. To estimate the resolution, we propose a mobile checkerboard analysis which allows to measure a lower bound resolution over the fault for an expected slip patch size and an specific stations deployment. We test ELADIN with synthetic examples and use it to invert the 2006 Guerrero Slow Slip Event (SSE). The later is one of the most studied Mexican SSE that unfortunately was recorded with only 15 stations, so a strong regularization is required. We compared our slip solution with two published slip models and found that our solution preserves the general characteristics observed by the other models such as an updip penetration of the SSE in the Guerrero seismic Gap. Despite this similarity, our resolution analysis indicates that this updip aseismic slip penetration might not be a reliable feature of the 2006 SSE.