Understanding the interaction between tectonic plates from geodetic data is relevant to the assessment of seismic hazard. To shed light on that prevalently slow aseismic interaction, we developed a new static-slip inversion strategy, the ELADIN (ELastostatic ADjoint INversion) method, that uses the adjoint elastostatic equations to compute the gradient of the cost function. To handle plausible slip constraints, ELADIN is a 2-step inversion algorithm. First it finds the slip that best explains the data without any constraint, and then refines the solution by imposing the constraints through a Gradient Projection Method. To obtain a selfsimilar, physically-consistent slip distribution that accounts for sparsity and uncertainty in the data, ELADIN reduces the model space by using a von Karman regularization function that controls the wavenumber content of the solution, and weights the observations according to their covariance using the data precision matrix. Since crustal deformation is the result of different concomitant interactions at the plate interface, ELADIN simultaneously determines the regions of the interface subject to both stressing (i.e., coupling) and relaxing slip regimes. For estimating the resolution, we introduce a mobile checkerboard that allows to determine lower-bound fault resolution zones for an expected slip-patch size and a given stations array. We systematically test ELADIN with synthetic inversions along the whole Mexican subduction zone and use it to invert the 2006 Guerrero Slow Slip Event (SSE), which is one of the most studied SSEs in Mexico. Since only 12 GPS stations recorded the event, careful regularization is thus required to achieve reliable solutions. We compared our preferred slip solution with two previously published models and found that our solution retains their most reliable features. In addition, although all three SSE models predict an upward slip penetration invading the seismogenic zone of the Guerrero seismic gap, our resolution analysis indicates that this penetration might not be a reliable feature of the 2006 SSE.