In a Carnot group G of step 2 and homogeneous dimension Q, we prove that almost minimizers of the (horizontal) one-phase p-Bernoulli-type functional J(p) (u , Omega) := integral(Omega) ( | del(G)u(x)|(p) + chi ({ u > 0 }) ( x )) dx whenever p > p(#) := 2Q/Q + 2, are locally Lipschitz continuous with respect Carnot-Carath & eacute;odory distance.
Ferrari, F., Merlino, E.M. (2026). Lipschitz regularity for almost minimizers of a one-phase p-Bernoulli-type functional in Carnot groups of step two. ADVANCES IN CALCULUS OF VARIATIONS, 19(4), 511-554 [10.1515/acv-2025-0024].
Lipschitz regularity for almost minimizers of a one-phase p-Bernoulli-type functional in Carnot groups of step two
Ferrari F.;Merlino E. M.
2026
Abstract
In a Carnot group G of step 2 and homogeneous dimension Q, we prove that almost minimizers of the (horizontal) one-phase p-Bernoulli-type functional J(p) (u , Omega) := integral(Omega) ( | del(G)u(x)|(p) + chi ({ u > 0 }) ( x )) dx whenever p > p(#) := 2Q/Q + 2, are locally Lipschitz continuous with respect Carnot-Carath & eacute;odory distance.File in questo prodotto:
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