s, p-Harmonic Approximation of Functions of Least Wˢˡ-Seminorm

We investigate the convergence as p↘1 of the minimizers of the Ws,p-energy for s∈(0,1) and p∈(1,∞) to those of the Ws,1-energy, both in the pointwise sense and by means of Γ-convergence. We also address the convergence of the corresponding Euler–Lagrange equations and the equivalence between minimizers and weak solutions. As ancillary results, we study some regularity issues regarding minimizers of the Ws,1-energy.