A control on the set where a Green's function vanishes
A note on lifting of Carnot groups.
We prove that every homogeneous Carnot group can be lifted to a free homogeneous Carnot group. Though following the ideas of Rothschild and Stein, we give simple and self-contained arguments, providing a constructive proof, as shown in the examples.
A remark on the uniqueness of fundamental solutions to the -Laplacian equation, .
A simple construction of a parametrix for a regular hyperbolic operator
An Elementary Proof of Harnack's Inequality for Schrödinger Operators and Related Topics.
An invariance method for constructing fundamental solutions for
Analysis of second order differential operators on Heisenberg groups. I.
Analysis of second order differential operators with complex coefficients on the Heisenberg group.
Analysis of the boundary symbol for the two-phase Navier-Stokes equations with surface tension
The two-phase free boundary value problem for the Navier-Stokes system is considered in a situation where the initial interface is close to a halfplane. We extract the boundary symbol which is crucial for the dynamics of the free boundary and present an analysis of this symbol. Of particular interest are its singularities and zeros which lead to refined mapping properties of the corresponding operator.
Analytic continuation of fundamental solutions to differential equations with constant coefficients
If is a polynomial in such that integrable, then the inverse Fourier transform of is a fundamental solution to the differential operator . The purpose of the article is to study the dependence of this fundamental solution on the polynomial . For it is shown that can be analytically continued to a Riemann space over the set of all polynomials of the same degree as . The singularities of this extension are studied.
Analytical solution for the time-fractional telegraph equation.
Analyticity of relative fundamental solutions and projections for left invariant operators on the Heisenberg group
Asymptotic Behavior of Fundamental Solutions and Potential Theory of Prabolic Operators with Variable Coeeficients.
Asymptotic behaviour of the weighted trace of the Schrödinger operator.
Asymptotics for some Green Kernels on the Heisenberg Group and the Martin Boundary.
Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type
We establish the existence, uniqueness and main properties of the fundamental solutions for the fractional porous medium equation introduced in [51]. They are self-similar functions of the form with suitable and . As a main application of this construction, we prove that the asymptotic behaviour of general solutions is represented by such special solutions. Very singular solutions are also constructed. Among other interesting qualitative properties of the equation we prove an Aleksandrov reflection...
Boundary value problems for quasielliptic equations in a half-space.
Cauchy problem for a class of parabolic systems of Shilov type with variable coefficients
In the case of initial data belonging to a wide class of functions including distributions of Gelfand-Shilov type we establish the correct solvability of the Cauchy problem for a new class of Shilov parabolic systems of equations with partial derivatives with bounded smooth variable lower coefficients and nonnegative genus. We also investigate the conditions of local improvement of the convergence of a solution of this problem to its limiting value when the time variable tends to zero.
Characterization of the solutions of a 2b-parabolic operator with initial data in BMO
Construction de solutions élémentaires dans le faisceau de M. Sato