On the Schrödinger equation in L...spaces.
On the Schrödinger heat kernel in horn-shaped domains
We prove pointwise lower bounds for the heat kernel of Schrödinger semigroups on Euclidean domains under Dirichlet boundary conditions. The bounds take into account non-Gaussian corrections for the kernel due to the geometry of the domain. The results are applied to prove a general lower bound for the Schrödinger heat kernel in horn-shaped domains without assuming intrinsic ultracontractivity for the free heat semigroup.
On the Schwarz algorithms for the elliptic exterior boundary value problems
Tuning the alternating Schwarz method to the exterior problems is the subject of this paper. We present the original algorithm and we propose a modification of it, so that the solution of the subproblem involving the condition at infinity has an explicit integral representation formulas while the solution of the other subproblem, set in a bounded domain, is approximated by classical variational methods. We investigate many of the advantages of the new Schwarz approach: a geometrical convergence...
On the Schwarz algorithms for the Elliptic Exterior Boundary Value Problems
Tuning the alternating Schwarz method to the exterior problems is the subject of this paper. We present the original algorithm and we propose a modification of it, so that the solution of the subproblem involving the condition at infinity has an explicit integral representation formulas while the solution of the other subproblem, set in a bounded domain, is approximated by classical variational methods. We investigate many of the advantages of the new Schwarz approach: a geometrical convergence...
On the search for singularities in incompressible flows
In these notes we give some examples of the interaction of mathematics with experiments and numerical simulations on the search for singularities.
On the second boundary value problem for equations of Monge-Ampère type.
On the second eigenvalue of a Hardy-Sobolev operator.
On the second order derivatives of convex functions on the Heisenberg group
In the euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result holds in the Heisenberg group, by showing that every continuous –convex function belongs to the class of functions whose second order horizontal distributional derivatives are Radon measures. Together with a recent result by Ambrosio and Magnani, this proves the existence a.e. of second order horizontal derivatives for...
On the second order slip Reynolds equation with molecular dynamics: existence and uniqueness.
On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes
Cell-centered and vertex-centered finite volume schemes for the Laplace equation with homogeneous Dirichlet boundary conditions are considered on a triangular mesh and on the Voronoi diagram associated to its vertices. A broken P1 function is constructed from the solutions of both schemes. When the domain is two-dimensional polygonal convex, it is shown that this reconstruction converges with second-order accuracy towards the exact solution in the L2 norm, under the sufficient condition that the...
On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes
Cell-centered and vertex-centered finite volume schemes for the Laplace equation with homogeneous Dirichlet boundary conditions are considered on a triangular mesh and on the Voronoi diagram associated to its vertices. A broken P1 function is constructed from the solutions of both schemes. When the domain is two-dimensional polygonal convex, it is shown that this reconstruction converges with second-order accuracy towards the exact solution in the L2 norm, under the sufficient condition that the...
On the semi-classical approximation of the solution of the Heisenberg equation with spin
On the Semigroup of the Stokes Operator for Exterior Domains in Lq-Spaces.
On the semigroups of age-size dependent population dynamcis with spatial diffusion.
On the set of solutions of some nonconvex nonclosed hyperbolic differential inclusions
We consider a class of nonconvex and nonclosed hyperbolic differential inclusions and we prove the arcwise connectedness of the solution set.
On the sets of regularity of solutions for a class of degenerate nonlinear elliptic fourth-order equations with data.
On the short time asymptotic of the stochastic Allen–Cahn equation
A description of the short time behavior of solutions of the Allen–Cahn equation with a smoothened additive noise is presented. The key result is that in the sharp interface limit solutions move according to motion by mean curvature with an additional stochastic forcing. This extends a similar result of Funaki [Acta Math. Sin (Engl. Ser.)15 (1999) 407–438] in spatial dimension n=2 to arbitrary dimensions.
On the sign of Colombeau functions and applications to conservation laws
A generalized concept of sign is introduced in the context of Colombeau algebras. It extends the sign of the point-value in the case of sufficiently regular functions. This concept of generalized sign is then used to characterize the entropy condition for discontinuous solutions of scalar conservation laws.
On the singular behavior of solutions of a transmission problem in a dihedral.
On the singular limit in a phase field model of phase transitions