Lipschitz regularity of a weakly coupled vectorial almost-minimizers for the p-Laplacian

For a given constant lambda>0 and a bounded Lipschitz domain D subset of R-n(n >= 2), we establish that almost-minimizers of the functional J(v;D)=(D)integral(m)& sum;(i=1)|del vi(x)|(p)+lambda chi{|v|>0}(x) dx, 1<p<infinity, where v=(v(1),<middle dot><middle dot><middle dot>,v(m)),and m is an element of N , and , exhibit optimal Lipschitz continuity in compact sets of D. Furthermore, assuming p >= 2 and employing a distinctly different methodology, we tackle the issue of boundary Lipschitz regularity for <bold>v</bold>. This approach simultaneously yields an alternative proof for the optimal local Lipschitz regularity for the interior case. (c) 2024The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)