We prove the local Lipschitz regularity of the minimizers of functionals of the form F(u)=∫_Ω f(∇u(x))+g(x)u(x)dx. u∈ϕ+W^{1,1}_0(Ω) where g is bounded and ϕ satisfies the Lower Bounded Slope Condition. The function f is assumed to be convex but not uniformly convex everywhere. As byproduct, we also prove the existence of a locally Lipschitz minimizer for a class of functionals of the type above but allowing to the function f to be nonconvex.
Local Lipschitz continuity of the minimizers of nonuniformly convex functionals under the Lower Bounded Slope Condition / Giannetti, Flavia; Treu, Giulia. - (2025). [10.48550/arXiv.2504.11594]
Local Lipschitz continuity of the minimizers of nonuniformly convex functionals under the Lower Bounded Slope Condition
Flavia Giannetti
;
2025
Abstract
We prove the local Lipschitz regularity of the minimizers of functionals of the form F(u)=∫_Ω f(∇u(x))+g(x)u(x)dx. u∈ϕ+W^{1,1}_0(Ω) where g is bounded and ϕ satisfies the Lower Bounded Slope Condition. The function f is assumed to be convex but not uniformly convex everywhere. As byproduct, we also prove the existence of a locally Lipschitz minimizer for a class of functionals of the type above but allowing to the function f to be nonconvex.File in questo prodotto:
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