Local Lipschitz continuity of the minimizers of nonuniformly convex functionals under the Lower Bounded Slope Condition
Abstract
Abstract We prove the local Lipschitz regularity of the minimizers of functionals of the form $$ \mathcal {I}(u)=\int _\Omega f(\nabla u(x))+g(x)u(x)\,dx\qquad u\in \phi +W^{1,1}_0(\Omega ) $$ I ( u ) = ∫ Ω f ( ∇ u ( x ) ) + g ( x ) u ( x ) d x u ∈ ϕ + W 0 1 , 1 ( Ω ) where g is bounded and $$\phi $$ ϕ satisfies the Lower Bounded Slope Condition. The function f is assumed to be convex but not uniformly convex everywhere. As a byproduct, we also prove the existence of a locally Lipschitz minimizer for a class of functionals of the type above but allowing the function f to be nonconvex.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Optimization and Variational Analysis
Numerical methods in inverse problems
Publication details
- Journal / source
- Calculus of Variations and Partial Differential Equations
- Volume
- 65
- Issue
- 5
- Publication date
- 24 April 2026
- Language
- EN