On the interior smoothness of solutions to second-order elliptic equations.
On the inverse problem of the Sturm-Liouville type for a linear elliptic partial differential equation with constant coefficients of the second order
On the inversion of pseudo-differential operators
On the iterated Green functions on a bounded domain and their related Kato class of potentials.
On the iterative construction of a solution of nonlinear elliptic boundary value problems
On the iterative solution of finite element systems of equations
On the iterative solution of some nonlinear evolution equations
On the jump set of solutions of the total variation flow
On the Keldyš-Fichera boundary-value problem for degenerate quasilinear elliptic equations.
On the Klainerman–Machedon conjecture for the quantum BBGKY hierarchy with self-interaction
We consider the 3D quantum BBGKY hierarchy which corresponds to the -particle Schrödinger equation. We assume the pair interaction is . For the interaction parameter , we prove that, provided an energy bound holds for solutions to the BBKGY hierarchy, the limit points satisfy the space-time bound conjectured by S. Klainerman and M. Machedon [45] in 2008. The energy bound was proven to hold for in [28]. This allows, in the case , for the application of the Klainerman–Machedon uniqueness theorem...
On the Korteweg-De Vries Equation.
On the Korteweg-de Vries equation: an associated equation.
On the Kuramoto-Sivashinsky equation in a disk
We consider the first initial-boundary value problem for the 2-D Kuramoto-Sivashinsky equation in a unit disk with homogeneous boundary conditions, periodicity conditions in the angle, and small initial data. Apart from proving the existence and uniqueness of a global in time solution, we construct it in the form of a series in a small parameter present in the initial conditions. In the stable case we also obtain the uniform in space long-time asymptotic expansion of the constructed solution and...
On the -instability of fluid flows
On the -decay and local energy decay of solutions to nonlinear Klein-Gordon equations
On the -regularity of solutions of nonlinear elliptic equations in Orlicz spaces.
On the lack of null-controllability of the heat equation on the half space.
On the Ladyzhenskaya-Smagorinsky turbulence model of the Navier-Stokes equations in smooth domains. The regularity problem
We establish regularity results up to the boundary for solutions to generalized Stokes and Navier–Stokes systems of equations in the stationary and evolutive cases. Generalized here means the presence of a shear dependent viscosity. We treat the case . Actually, we are interested in proving regularity results in spaces for all the second order derivatives of the velocity and all the first order derivatives of the pressure. The main aim of the present paper is to extend our previous scheme, introduced...
On the Laguerre calculus of left-invariant convolution (pseudo-differential) operators on the Heisenberg group
On the Landau approximation in plasma physics