Related papers: Complex $\Gamma$-convergence and magnetic Dirichle…

Motivated by the work of Cappell, Deturck, Gluch and Miller, we extend the notion of cohomology of harmonic forms (of a compact manifold with boundary) to the abstract setting of Hilbert complexes. Then, we present some geometric…

This paper addresses the asymptotic development of order 2 by Gamma convergence of the Cahn-Hillard functional with Dirichlet boundary conditions, where the potential has subquadratic growth near the wells.

The concept of reiterated $\Sigma$-convergence (and more generally of multiscale $\Sigma$-convergence) is extended to framework of Orlicz-Sobolev spaces, in order to deals with homogenization of multiscales problems in general deterministic…

We consider second order phase field functionals, in the continuum setting, and their discretization with isogeometric tensor product B-splines. We prove that these functionals, continuum and discrete, $\Gamma$-converge to a brittle…

We elaborate a new method for constructing traces of quadratic forms in the framework of Hilbert and Dirichlet spaces. Our method relies on monotone convergence of quadratic forms and the canonical decomposition into regular and singular…

We show that an isometric action of a torsion-free uniform lattice $\Gamma$ on hyperbolic space $\mathbb{H}^n$ can be metrically approximated by geometric actions of $\Gamma$ on $\mathrm{CAT}(0)$ cube complexes, provided that either $n$ is…

We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…

We derive, by means of variational techniques, a limiting description for a class of integral functionals under linear differential constraints. The functionals are designed to encode the energy of a high-contrast composite, that is, a…

For $\Omega \subset \mathbb{R}^n$, a convex and bounded domain, we study the spectrum of $-\Delta_\Omega$ the Dirichlet Laplacian on $\Omega$. For $\Lambda\geq0$ and $\gamma \geq 0$ let $\Omega_{\Lambda, \gamma}(\mathcal{A})$ denote any…

We study the Dirichlet problem for the Lagrangian phase operator, in both the real and complex setting. Our main result states that if $\Omega$ is a compact domain in $\mathbb{R}^{n}$ or $\mathbb{C}^n$, then there exists a solution to the…

In the framework of Hilbert spaces we shall give necessary and sufficient conditions to define a Dirichlet-to-Neumann operator via Dirichlet principle. For singular Dirichlet-to-Neumann operators we will establish Laurent expansion near…

We reconsider the Bargmann-Dirichlet space on the complex plane $\mathbb{C}$ and its generalizations considered in [8]. Concretely, we first present a new characterization of such spaces as harmonic spaces of the magnetic Laplacian with…

In contrast with the well-known methods of matching asymptotics and multiscale (or compound) asymptotics, the " functional analytic approach " of Lanza de Cristoforis (Analysis 28, 2008) allows to prove convergence of expansions around…

We consider a class of fully nonlinear nonlocal degenerate elliptic operators which are modeled on the fractional Laplacian and converge to the truncated Laplacians. We investigate the validity of (strong) maximum and minimum principles,…

This paper continues the study of the asymptotic development of order 2 by $\Gamma$ -convergence of the Cahn-Hilliard functional with Dirichlet boundary conditions initiated in [8]. While in the first paper, the Dirichlet data are assumed…

For a given self-adjoint first order elliptic differential operator on a closed smooth manifold, we prove a list of results on when the delocalized eta invariant associated to a regular covering space can be approximated by the delocalized…

We study semigroups of convex monotone operators on spaces of continuous functions and their behaviour with respect to $\Gamma$-convergence. In contrast to the linear theory, the domain of the generator is, in general, not invariant under…

We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…

We derive constraints on Lagrangian embeddings in completions of certain stable symplectic fillings with semisimple symplectic cohomologies. Manifolds with these properties can be constructed by generalizing the boundary connected sum…

We study the solution of minimax problems $\min_x \max_y G(x) + \langle K(x),y\rangle - F^*(y)$ in finite-dimensional Hilbert spaces. The functionals $G$ and $F^*$ we assume to be convex, but the operator $K$ we allow to be non-linear. We…