$(s,p)$-harmonic approximation of functions of least $W^{s,1}$-seminorm

Abstract

We investigate the convergence as $p\searrow 1$ of the minimizers of the $W^{s,p}$-energy for $s\in (0,1)$ and $p\in (1,\infty )$ to those of the $W^{s,1}$-energy, both in the pointwise sense and by means of $\Gamma$-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 $W^{s,1}$-energy.

43 pages

References in corpus (2)

• Gamma-convergence of nonlocal perimeter functionals
• Asymptotics of Dirichlet Problems to Fractional p-Laplacian Functionals-Approach in De Giorgi Sense