Related papers: A variational method for $\Phi^4_3$
We prove that in many cases the existence of an extremal metric for some Laplace eigenvalue in a conformal class allows to find extremal metrics in conformal classes close by. As a consequence and as part of the arguments we obtain…
A self-consistent renormalization group flow equation for the scalar lambda phi^4 theory is analyzed and compared with the local potential approximation. The two prescriptions coincide in the sharp cutoff limit but differ with a smooth…
The $\Phi^4_3$ measure is one of the easiest non-trivial examples of a Euclidean quantum field theory (EQFT) whose rigorous construction in the 1970's has been one of the celebrated achievements of constructive quantum field theory. In…
The Laplace transform is a useful and powerful analytic tool with applications to several areas of applied mathematics, including differential equations, probability and statistics. Similarly to the inversion of the Fourier transform,…
A finite-size scaling theory for the $\phi^4_4$ model is derived using renormalization group methods. Particular attention is paid to the partition function zeroes, in terms of which all thermodynamic observables can be expressed. While the…
We consider a general optimal control problem in the setting of gradient flows. Two approximations of the problem are presented, both relying on the variational reformulation of gradient-flow dynamics via the Weighted-Energy-Dissipation…
We provide a rigorous justification of the classical linearization approach in plasticity. By taking the small-deformations limit, we prove via \Gamma-convergence for rate-independent processes that energetic solutions of the quasi-static…
In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By the adjoint system…
In this paper we consider an intrinsic point of view to describe the equations of motion for higher-order variational problems with constraints on higher-order trivial principal bundles. Our techniques are an adaptation of the classical…
We prove a large deviation principle for a sequence of point processes defined by Gibbs probability measures on a Polish space. This is obtained as a consequence of a more general Laplace principle for the non-normalized Gibbs measures. We…
We describe a new method in lattice field theory to compute observables at various values of the parameters lambda_i in the action S[phi,lambda_i]. Firstly one performs a single simulation of a ``reference action'' S[phi^r, lambda_i^r] with…
We give a direct construction of invariant measures and global flows for the stochastic quantization equation to the quantum field theoretical $\Phi ^4_3$-model on the $3$-dimensional torus. This stochastic equation belongs to a class of…
We propose a numerical method to approximate the exact averaged boundary control of a family of wave equations depending on an unknown parameter sigma. More precisely the control, independent of sigma, that drives an initial data to a…
This paper is concerned with the Dirichlet eigenvalue problem for Laplace operator in a bounded domain with periodic perforation in the case of small volume. We obtain the optimal quantitative error estimates independent of the spectral…
We deal with the convergence of the value function of an approximate control problem with uncertain dynamics to the value function of a nonlinear optimal control problem. The assumptions on the dynamics and the costs are rather general and…
A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external…
This paper studies a {\it reversible} investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good. Our model allows for general diffusion dynamics on the demand as…
In this work we study the asymptotic distribution of eigenvalues in one-dimensional open sets. The method of proof is rather elementary, based on the Dirichlet lattice points problem, which enable us to consider sets with infinite measure.…
Multiscale analysis of a degenerate pseudoparabolic variational inequality, modelling the two-phase flow with dynamical capillary pressure in a perforated domain, is the main topic of this work. Regularisation and penalty operator methods…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…