Optimal local Lipschitz regularity for scalar almost minimizers of two-phase free-boundary functionals F(v;Ω):=\int φ(x,|∇v|)+λ_1χ{v<0}+λ_2χ{v>0}+min{λ_1,λ_2}χ{v=0}dx, with growth function φ a generalized Orlicz function and λ_1, λ_2 nonnegative bounded functions, is established, assuming a “small” density for either the positivity or the negativity set.
Lipschitz regularity of almost-minimizers in two-phase free boundary problems with generalized Orlicz growth
Francesco Solombrino;
2026-01-01
Abstract
Optimal local Lipschitz regularity for scalar almost minimizers of two-phase free-boundary functionals F(v;Ω):=\int φ(x,|∇v|)+λ_1χ{v<0}+λ_2χ{v>0}+min{λ_1,λ_2}χ{v=0}dx, with growth function φ a generalized Orlicz function and λ_1, λ_2 nonnegative bounded functions, is established, assuming a “small” density for either the positivity or the negativity set.File in questo prodotto:
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