The L.P.D.E.M., a mixed finite difference method for elliptic problems.
The -Wright function in time-fractional diffusion processes: a tutorial survey.
The magnetic Schrödinger operator and reverse Hölder class
The mathematical theory of low Mach number flows
The mathematical theory of the passage from compressible to incompressible fluid flow is reviewed.
The mathematical theory of low Mach number flows
The mathematical theory of the passage from compressible to incompressible fluid flow is reviewed.
The mathematics of large atoms
The mathematics of suspensions: Kac walks and asymptotic analyticity.
The maximum principle for equations with composite coefficients.
The Maxwell equation in a periodic medium : homogenization of the energy density
The mean curvature measure
We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is weakly continuous with respect to almost everywhere convergence. We also establish a sharp Harnack inequality for the minimal surface equation, which is crucial for our proof of the weak continuity. As an application we prove the existence of weak solutions to the...
The mean curvature of a Lipschitz continuous manifold
The paper is devoted to the description of some connections between the mean curvature in a distributional sense and the mean curvature in a variational sense for several classes of non-smooth sets. We prove the existence of the mean curvature measure of by using a technique introduced in [4] and based on the concept of variational mean curvature. More precisely we prove that, under suitable assumptions, the mean curvature measure of is the weak limit (in the sense of distributions) of the mean...
The mean-field limit for the dynamics of large particle systems
This short course explains how the usual mean-field evolution PDEs in Statistical Physics - such as the Vlasov-Poisson, Schrödinger-Poisson or time-dependent Hartree-Fock equations - are rigorously derived from first principles, i.e. from the fundamental microscopic models that govern the evolution of large, interacting particle systems.
The method of characteristics for hyperbolic boundary value problems on the plane.
The method of discretization in time and partial differential equations
The method of fictitious domains in the Signorini problem.
The method of fictitious right-hand sides
The paper deals with the application of a fast algorithm for the solution of finite-difference systems for boundary-value problems on a standard domain (e.g. on a rectangle) to the solution of a boundary-value problem on a domain of general shape contained in the standard domain. A simple iterative procedure is suggested for the determination of fictitious right-hand sides for the system on the standard domain so that its solution is the desired one. Under the assumptions that are usual for matrices...
The Method of Fractional Steps for Conservation Laws.
The method of least squares on the boundary and very weak solutions of the first biharmonic problem
The method of lines for hyperbolic stochastic functional partial differential equations
We apply an approximation by means of the method of lines for hyperbolic stochastic functional partial differential equations driven by one-dimensional Brownian motion. We study the stability with respect to small -perturbations.
The Method of Lines for Nonlinear Parabolic Differential Equations with Mixed Derivatives.