An existence result in nonlinear theory of electromagnetic fields
This paper is concerned with the nonlinear theory of equilibrium for materials which do not conduct electricity. An existence and uniqueness result is established.
An Existence Theorem for Class of Non-Coercive Optimization and Variational Problems.
An invariance method for constructing fundamental solutions for
An isoperimetric bound for a Sobolev constant
An iteration method for nonlinear second order evolution equations
Analyse 2-microlocale et équations d'Euler incompressible
Analyse microlocale et équations d’évolution
Analyse semi-classique pour l'équation de Harper. II: Comportement semi-classique près d'un rationnel
Analysis of a semidiscrete scheme for solving image smoothing equation of mean curvature flow type.
Analysis of a time discretization scheme for a nonstandard viscous Cahn–Hilliard system
In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase fields are the order parameter and the chemical potential. The initial and boundary-value problem for the evolutionary system is known to be well posed. Convergence of the discrete scheme to the solution of the continuous problem is proved by a careful development...
Analysis of second order differential operators on Heisenberg groups. I.
Analysis of second order differential operators with complex coefficients on the Heisenberg group.
Analysis of the boundary symbol for the two-phase Navier-Stokes equations with surface tension
The two-phase free boundary value problem for the Navier-Stokes system is considered in a situation where the initial interface is close to a halfplane. We extract the boundary symbol which is crucial for the dynamics of the free boundary and present an analysis of this symbol. Of particular interest are its singularities and zeros which lead to refined mapping properties of the corresponding operator.
Analysis of total variation flow and its finite element approximations
We study the gradient flow for the total variation functional, which arises in image processing and geometric applications. We propose a variational inequality weak formulation for the gradient flow, and establish well-posedness of the problem by the energy method. The main idea of our approach is to exploit the relationship between the regularized gradient flow (characterized by a small positive parameter , and the minimal surface flow [21] and the prescribed mean curvature flow [16]. Since our...
Analysis of total variation flow and its finite element approximations
We study the gradient flow for the total variation functional, which arises in image processing and geometric applications. We propose a variational inequality weak formulation for the gradient flow, and establish well-posedness of the problem by the energy method. The main idea of our approach is to exploit the relationship between the regularized gradient flow (characterized by a small positive parameter ε, see (1.7)) and the minimal surface flow [21] and the prescribed mean curvature flow [16]. Since...
Analytic and Gevrey Hypoellipticity
Analytic approximation for homogeneous solutions of linear PDE's
Analytic continuation of fundamental solutions to differential equations with constant coefficients
If is a polynomial in such that integrable, then the inverse Fourier transform of is a fundamental solution to the differential operator . The purpose of the article is to study the dependence of this fundamental solution on the polynomial . For it is shown that can be analytically continued to a Riemann space over the set of all polynomials of the same degree as . The singularities of this extension are studied.
Analytic Hypo-Ellipticity and Propagation of Regularity for a System of Microdifferential Equations with Non-Involutory Characteristics.
Analytic semigroups generated on a functional extrapolation space by variational elliptic equations
We prove that any elliptic operator of second order in variational form is the infinitesimal generator of an analytic semigroup in the functional space consinsting of all derivatives of hölder-continuous functions in where is a domain in not necessarily bounded. We characterize, moreover the domain of the operator and the interpolation spaces between this and the space . We prove also that the spaces can be considered as extrapolation spaces relative to suitable non-variational operators....