On the existence of a fundamental solution for a parabolic differential equation with unbounded coefficients
On the Fejér-F. Riesz inequality in
On the global well-posedness of the Boussinesq system with zero viscosity
In this paper we prove the global well-posedness of the two-dimensional Boussinesq system with zero viscosity for rough initial data.
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 local behaviour of solutions of a certain class of doubly nonlinear parabolic equations.
On the long-time behaviour of solutions of the p-Laplacian parabolic system
Convergence of global solutions to stationary solutions for a class of degenerate parabolic systems related to the p-Laplacian operator is proved. A similar result is obtained for a variable exponent p. In the case of p constant, the convergence is proved to be , and in the variable exponent case, L² and -weak.
On the optimality of velocity averaging lemmas
On the parameter dependence of solutions to the ...-equation.
On the Partial Regularity of Weak Solutions of Nonlinear Parabolic Systems.
On the precise asymptotics of the constant in Friedrich's inequality for functions vanishing on the part of the boundary with microinhomogeneous structure.
On the rate of the volume growth for symmetric viscous heat-conducting gas flows with a free boundary.
On the regularity of averages over spheres for kinetic transport equations in hyperbolic Sobolev spaces.
On the rigidity of minimal mass solutions to the focusing mass-critical NLS for rough initial data.
On the Schauder estimates of solutions to parabolic equations
On the Schrödinger equation in L...spaces.
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 solvability of a nonlocal problem arising in dynamics of moisture transfer.
On the solvability of nonlocal pluriparabolic problems.
On the solvability of parabolic and hyperbolic problems with a boundary integral condition.
On the stability of the Dirichlet problem for the vibrating string equation