Regularity of the optimal shape for the first eigenvalue of the laplacian with volume and inclusion constraints
Regularity of the Singular Sets of Two-Dimensional Area-Minimizing Flat Chains Modulo 3 in R3.
Regularity properties of free discontinuity sets
Regularity properties of optimal segmentations.
Regularity properties of optimal transportation problems arising in hedonic pricing models
We study a form of optimal transportation surplus functions which arise in hedonic pricing models. We derive a formula for the Ma–Trudinger–Wang curvature of these functions, yielding necessary and sufficient conditions for them to satisfy (A3w). We use this to give explicit new examples of surplus functions satisfying (A3w), of the form b(x,y) = H(x + y) where H is a convex function on ℝn. We also show that the distribution of equilibrium contracts in this hedonic pricing model is absolutely continuous...
Regularity properties of the distance functions to conjugate and cut loci for viscosity solutions of Hamilton-Jacobi equations and applications in Riemannian geometry
Given a continuous viscosity solution of a Dirichlet-type Hamilton-Jacobi equation, we show that the distance function to the conjugate locus which is associated to this problem is locally semiconcave on its domain. It allows us to provide a simple proof of the fact that the distance function to the cut locus associated to this problem is locally Lipschitz on its domain. This result, which was already an improvement of a previous one by Itoh and Tanaka [Trans. Amer. Math. Soc. 353 (2001) 21–40],...
Regularity results for a class of obstacle problems
We prove some optimal regularity results for minimizers of the integral functional belonging to the class , where is a fixed function, under standard growth conditions of -type, i.e.
Regularity results for a class of quasiconvex functionals with nonstandard growth
Regularity results for an optimal design problem with a volume constraint
Regularity results for minimal configurations of variational problems involving both bulk and surface energies and subject to a volume constraint are established. The bulk energies are convex functions with p-power growth, but are otherwise not subjected to any further structure conditions. For a minimal configuration (u,E), Hölder continuity of the function u is proved as well as partial regularity of the boundary of the minimal set E. Moreover, full regularity of the boundary of the minimal set...
Regularity results for anisotropic image segmentation models
Regularity results for minimizing currents with a free boundary.
Regularization and iterative methods for monotone variational inequalities.
Regularization inertial proximal point algorithm for monotone hemicontinuous mapping and inverse strongly monotone mappings in Hilbert spaces.
Regularization of a unilateral obstacle problem on the boundary.
Regularization of linear least squares problems by total bounded variation
Regularization of linear least squares problems by total bounded variation
We consider the problem : (P) Minimize over u ∈ K ∩ X, where α≥ 0, β > 0, K is a closed convex subset of L2(Ω), and the last additive term denotes the BV-seminorm of u, T is a linear operator from L2 ∩ BV into the observation space Y. We formulate necessary optimality conditions for (P). Then we show that (P) admits, for given regularization parameters α and β, solutions which depend in a stable manner on the data z. Finally we study the asymptotic behavior when α = β → 0. The regularized...
Regularization of noncoercive constraints in Hencky plasticity
The aim of this paper is to find the largest lower semicontinuous minorant of the elastic-plastic energy of a body with fissures. The functional of energy considered is not coercive.
Regularization parameter selection in discrete ill-posed problems - the use of the U-curve
To obtain smooth solutions to ill-posed problems, the standard Tikhonov regularization method is most often used. For the practical choice of the regularization parameter α we can then employ the well-known L-curve criterion, based on the L-curve which is a plot of the norm of the regularized solution versus the norm of the corresponding residual for all valid regularization parameters. This paper proposes a new criterion for choosing the regularization parameter α, based on the so-called U-curve....
Reinforcement problems in the calculus of variations
Relación entre conos de direcciones decrecientes y conos de direcciones de descenso.
Sea f: N → R una función convexa y sea x ∈ Ni, donde N es un convexo en un espacio vectorial real. Se demuestra que, si Df<(x) es no vacío, entonces Df<(x) es el interior algebraico de Df≤(x).