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.
s, p-Harmonic Approximation of Functions of Least Wˢˡ-Seminorm / C. Bucur, S. Dipierro, L. Lombardini, J.M. Mazón, E. Valdinoci. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - (2021). [Epub ahead of print] [10.1093/imrn/rnab284]
s, p-Harmonic Approximation of Functions of Least Wˢˡ-Seminorm
C. BucurPrimo
;S. Dipierro
Secondo
;L. Lombardini;E. ValdinociUltimo
2021
Abstract
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.
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