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Abstract Oceanic detachment faults represent an end-member form of seafloor creation, associated with relatively weak magmatism at slow-spreading mid-ocean ridges. We use 3-D numerical models to investigate the underlying mechanisms for why detachment faults predominantly form on the transform side (inside corner) of a ridge-transform intersection as opposed to the fracture zone side (outside corner). One hypothesis for this behavior is that the slipping, and hence weaker, transform fault allows for the detachment fault to form on the inside corner, and a stronger fracture zone prevents the detachment fault from forming on the outside corner. However, the results of our numerical models, which simulate different frictional strengths in the transform and fracture zone, do not support the first hypothesis. Instead, the model results, combined with evidence from rock physics experiments, suggest that shear-stress on transform fault generates excess lithospheric tension that promotes detachment faulting on the inside corner. 

This work aims to prove a Hardy-type inequality and a trace theorem for a class of function spaces on smooth domains with a nonlocal character. Functions in these spaces are allowed to be as rough as an [Formula: see text]-function inside the domain of definition but as smooth as a [Formula: see text]-function near the boundary. This feature is captured by a norm that is characterized by a nonlocal interaction kernel defined heterogeneously with a special localization feature on the boundary. Thus, the trace theorem we obtain here can be viewed as an improvement and refinement of the classical trace theorem for fractional Sobolev spaces [Formula: see text]. Similarly, the Hardy-type inequalities we establish for functions that vanish on the boundary show that functions in this generalized space have the same decay rate to the boundary as functions in the smaller space [Formula: see text]. The results we prove extend existing results shown in the Hilbert space setting with p = 2. A Poincaré-type inequality we establish for the function space under consideration together with the new trace theorem allows formulating and proving well-posedness of a nonlinear nonlocal variational problem with conventional local boundary condition.