9 papers
Good access to the crack and integrability of the full gradient for Griffith almost-minimizers in the plane
Camille Labourie, Lorenzo Lamberti, Antoine Lemenant
We show that, for almost-minimizers of the Griffith energy in the plane, the complement of the crack is locally covered by a finite number of John domains where the displacement sa…
Morrey estimates for the gradient in non-linear variational transmission problems
Luca Esposito, Lorenzo Lamberti
We study a class of variational transmission problems driven by nonlinear energies with discontinuous coefficients across a prescribed interface. The model setting consists of inte…
Ahlfors-regularity for minimizers of a multiphase optimal design problem
Luca Esposito, Lorenzo Lamberti, Giovanni Pisante
We establish an Alhfors-regularity result for minimizers of a multiphase optimal design problem. It is a variant of the classical variational problem which involves a finite number…
Quantitative regularity properties for the optimal design problem
Lorenzo Lamberti, Antoine Lemenant
In this paper we slightly improve the regularity theory for the so called optimal design problem. We first establish the uniform rectifiability of the boundary of the optimal set,…
Finsler -Laplacian in domains becoming unbounded
Luca Esposito, Lorenzo Lamberti, Dattatreya N. N. +1
We study the asymptotic behavior of sequences of solutions, energies functionals, and the first eigenvalues associated with the Finsler -Laplace operator, also known as the anis…
Quasiconvex Bulk and Surface Energies with subquadratic growth
Menita Carozza, Luca Esposito, Lorenzo Lamberti
We establish partial Hölder continuity of the gradient for equilibrium configurations of vectorial multidimensional variational problems, involving bulk and surface energies. The b…
Regularity results for almost-minimizers of anisotropic free interface problem with Hölder dependence on the position
Luca Esposito, Lorenzo Lamberti, Giovanni Pisante
We establish regularity results for almost-minimizers of a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type. The surfa…
Regularity Results for a free interface problem with Hölder coefficients
Luca Esposito, Lorenzo Lamberti
We study a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type albeit of very general form allowing the dependence from t…
Variational analysis in one and two dimensions of a frustrated spin system: chirality transitions and magnetic anisotropic transitions
Andrea Kubin, Lorenzo Lamberti
We study the energy of a ferromagnetic/antiferromagnetic frustrated spin system with values on two disjoint circumferences of the 3-dimensional unit sphere in a one-dimensional and…