EDPS paraboliques à coefficients non—lipschitziens avec réflexion
EDSR, convergence en loi et homogénéisation d'EDP paraboliques semi-linéaires
Eigenfunctions and fundamental solutions of the fractional two-parameter Laplacian.
Eigenvalue distribution of random operators and matrices
Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle for the discrete case
A discretized boundary value problem for the Laplace equation with the Dirichlet and Neumann boundary conditions on an equilateral triangle with a triangular mesh is transformed into a problem of the same type on a rectangle. Explicit formulae for all eigenvalues and all eigenfunctions are given.
Einige elementare Ungleichungen für Exponentialpolynome.
Elastic wave equation
The goal of this talk is to describe the Lamé operator which drives the propagation of linear elastic waves. The main motivation for me is the work I have done in collaboration with Michel Campillo’s group from LGIT (Grenoble) on passive imaging in seismology. From this work, several mathematical problems emerged: equipartition of energy between and waves, high frequency description of surface waves in a stratified medium and related inverse spectral problems.We discuss the following topics:What...
Electrical impedance tomography in nonlinear media
Eliptické parciální diferenciální rovnice s degenerovanými koeficienty
Elliptic boundary problems on spaces with conic points
Elliptic boundary value problem in Vanishing Mean Oscillation hypothesis
In this note the well-posedness of the Dirichlet problem (1.2) below is proved in the class for all and, as a consequence, the Hölder regularity of the solution . is an elliptic second order operator with discontinuous coefficients and the lower order terms belong to suitable Lebesgue spaces.
Elliptic equations of higher stochastic order
This paper discusses analytical and numerical issues related to elliptic equations with random coefficients which are generally nonlinear functions of white noise. Singularity issues are avoided by using the Itô-Skorohod calculus to interpret the interactions between the coefficients and the solution. The solution is constructed by means of the Wiener Chaos (Cameron-Martin) expansions. The existence and uniqueness of the solutions are established under rather weak assumptions, the main of which...
Elliptic Equations with Noninvertible Fredholm Linear Part and Bounded Nonlinearities.
Elliptic problems with integral diffusion
In this paper, we review several recent results dealing with elliptic equations with non local diffusion. More precisely, we investigate several problems involving the fractional laplacian. Finally, we present a conformally covariant operator and the associated singular and regular Yamabe problem.
Embeddedness and uniqueness of minimal surfaces solving a partially free boundary value problem.
Embedding operators and maximal regular differential-operator equations in Banach-valued function spaces.
Embedding theorems in Banach-valued -spaces and maximal -regular differential-operator equations.
Enclosure of solutions for elliptic boundary value problems with nonmonotone discontinuous nonlinearity
Energy quantization and mean value inequalities for nonlinear boundary value problems
We give a unified statement and proof of a class of well known mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on the normal derivative at the boundary. These inequalities give rise to an energy quantization principle for sequences of solutions of boundary value problems that have bounded energy and whose energy densities satisfy nonlinear bounds on the Laplacian and normal...
Enhanced electrical impedance tomography via the Mumford–Shah functional
We consider the problem of electrical impedance tomography where conductivity distribution in a domain is to be reconstructed from boundary measurements of voltage and currents. It is well-known that this problem is highly illposed. In this work, we propose the use of the Mumford–Shah functional, developed for segmentation and denoising of images, as a regularization. After establishing existence properties of the resulting variational problem, we proceed by demonstrating the approach in several...