Rescaled (s,p)-Gagliardo energies Gamma-converge to a pairwise difference double integral as s to 0+ and to the Dirichlet p-energy as s to 1-, with equispaced jumps minimizing the energy among piecewise affine periodic functions in 1D.
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$\Gamma$-convergence, variational analysis and characterisation of minimisers for $(s,p)$-Gagliardo energies in the flat $d$-torus
Rescaled (s,p)-Gagliardo energies Gamma-converge to a pairwise difference double integral as s to 0+ and to the Dirichlet p-energy as s to 1-, with equispaced jumps minimizing the energy among piecewise affine periodic functions in 1D.