On the Equation of Surfaces of Prescribed Mean Curvature. Existence and Uniqueness without Boundary Conditions.
On the equation in planar domains
The blow-up of solutions for a parabolic equation with nonlocal exponential nonlinearity is studied.
On the equations of ideal incompressible magneto-hydrodynamics
On the equivalence of Green functions for general Schrödinger operators on a half-space
We consider the general Schrödinger operator on a half-space in ℝⁿ, n ≥ 3. We prove that the L-Green function G exists and is comparable to the Laplace-Green function provided that μ is in some class of signed Radon measures. The result extends the one proved on the half-plane in [9] and covers the case of Schrödinger operators with potentials in the Kato class at infinity considered by Zhao and Pinchover. As an application we study the cone of all positive L-solutions continuously vanishing...
On the equivalence of primal and dual substructuring preconditioners.
On the error term in Weyl's law for Heisenberg manifolds
On the essential spectrum and eigenvalue asymptotics of certain Schrödinger operators
On the essential spectrum of Dirac operators with spherically symmetric potentials.
On the essential spectrum of many-particle pseudorelativistic Hamiltonians with permutational symmetry account.
On the Essential Spectrum of Schrödinger Operators with Spherically Symmetric Potentials.
On the Estimates of the Convergence Rate of the Finite Difference Schemes for the Approximation of Solutions of Hyperbolic Problems
On the Estimates of the Convergence Rate of the Finite Difference Schemes for the Approximation of Solutions of Hyperbolic Problems, II Part
On the Euler equations of incompressible perfect fluids
On the Euler equations with a singular external velocity field
On the evolution equations of viscous gaseous stars
On the exact controllability of a nonlinear stochastic heat equation.
On the exact WKB analysis of microdifferential operators of WKB type
We first introduce the notion of microdifferential operators of WKB type and then develop their exact WKB analysis using microlocal analysis; a recursive way of constructing a WKB solution for such an operator is given through the symbol calculus of microdifferential operators, and their local structure near their turning points is discussed by a Weierstrass-type division theorem for such operators. A detailed study of the Berk-Book equation is given in Appendix.
On the existence and regularity of solutions of linear equations in spaces
On the existence and regularity of solutions to the problem of transmission
On the existence and regularity of the solutions to the incompressible Navier-Stokes equations in presence of mass diffusion
This paper is devoted to the study of the incompressible Navier-Stokes equations with mass diffusion in a bounded domain in R³ with C³ boundary. We prove the existence of weak solutions, in the large, and the behavior of the solutions as the diffusion parameter λ → 0. Moreover, the existence of L²-strong solution, in the small, and in the large for small data, is proved. Asymptotic regularity (the regularity after a finite period) of a weak solution is studied. Finally, using the Dore-Venni theory,...