Some approximation properties in Orlicz-Sobolev spaces
Some aspects of holomorphic approximations from the point of view of PDEs
Some aspects of the variational nature of mean curvature flow
We show that the classical solution of the heat equation can be seen as the minimizer of a suitable functional defined in space-time. Using similar ideas, we introduce a functional on the class of space-time tracks of moving hypersurfaces, and we study suitable minimization problems related with . We show some connections between minimizers of and mean curvature flow.
Some asymptotic error estimates for finite element approximation of minimal surfaces
Some asymptotic formulae for spectra of a general convex domain.
Some asymptotic problems in fully nonlinear elliptic equations and stochastic control
Some boundary problems for the equations with strong degeneration
Some boundary value problems for systems of linear partial differential equations of hyperbolic type.
Some calculus with extensive quantities: Wave equation.
Some classes of inverse evolution problems for parabolic equations.
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
We consider three types of semilinear second order PDEs on a cylindrical domain , where is a bounded domain in , . Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of is reserved for time , the third type is an elliptic equation with a singled out unbounded variable . We discuss the asymptotic behavior, as , of solutions which are defined and bounded on .
Some compactness methods in the theory of nonlinear evolution equations with applications to P.D.E.
Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem
We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads...
Some constancy results for harmonic maps from non-contractable domains into spheres.
Some constancy results for nematic liquid crystals and harmonic maps
Some constructive applications of -representations to integration of PDEs
Two new applications of -representations of PDEs are presented: 1. Geometric algorithms for numerical integration of PDEs by constructing planimetric discrete nets on the Lobachevsky plane . 2. Employing -representations for the spectral-evolutionary problem for nonlinear PDEs within the inverse scattering problem method.
Some continuation properties via minimax arguments.
Some controllability results for the 2D Kolmogorov equation
Some controllability results for the relativistic Vlasov-Maxwell system
The goal of this note is to present the recent results concerning the controllability of the Vlasov-Maxwell system, which are proved in the paper [10] by Olivier Glass and the author.