We consider generalized solutions of the Perona–Malik equation in dimension one, defined
as all possible limits of solutions to the semidiscrete approximation in which derivatives with …

We consider the Perona-Malik functional in dimension one, namely an integral functional
whose Lagrangian is convex-concave with respect to the derivative, with a convexification …

We study Radon measure‐valued solutions of the Cauchy–Dirichlet problem for∂ tu= Δ ϕ
(u) ∂_tu=Δϕ(u) for a continuous, nondecreasing, at most powerlike ϕ ϕ. We prove well …

We consider generalized solutions of the Perona-Malik equation in dimension one, defined
as all possible limits of solutions to the semi-discrete approximation in which derivatives with …

We study the initial–boundary value problem ut=[φ (u)] x x+ ϵ [ψ (u)] txx in Ω×(0, T) φ (u)+ ϵ
[ψ (u)] t= 0 in∂ Ω×(0, T) u= u 0 in Ω×{0}, where Ω is an interval and u 0 is a nonnegative …

We continue the asymptotic analysis of minimizers for the singularly perturbed Perona-Malik
functional in dimension one that we started in a previous paper, in which we had shown that …

Abstract We consider the Perona-Malik equation, which is a forward-backward parabolic
equation that can be seen as the formal gradient-flow of a non-convex functional, and we …

This text on measure theory with applications to partial differential equations covers general
measure theory, Lebesgue spaces of real-valued and vector-valued functions, different …

This paper analyzes several key technical problems to intelligent flight by means of
modeling analysis and scientific demonstration, and finally puts forward the construction …