On a Parabolic Symmetry Problem.
On a singular sublinear polyharmonic problem.
On smoothness of a fundamental solution to a second order hyperbolic equation.
On some quasimetrics and their applications.
On splitting up singularities of fundamental solutions to elliptic equations in ℂ2
It is known that the fundamental solution to an elliptic differential equation with analytic coefficients exists, is determined up to the kernel of the differential operator, and has singularities on characteristics of the equation in ℂ2. In this paper we construct a representation of fundamental solution as a sum of functions, each of those has singularity on a single characteristic.
On the asymptotic behavior for convection-diffusion equations associated to higher order elliptic operators in divergence form.
We consider the linear convection-diffusion equation associated to higher order elliptic operators⎧ ut + Ltu = a∇u on Rnx(0,∞)⎩ u(0) = u0 ∈ L1(Rn),where a is a constant vector in Rn, m ∈ N*, n ≥ 1 and L0 belongs to a class of higher order elliptic operators in divergence form associated to non-smooth bounded measurable coefficients on Rn. The aim of this paper is to study the asymptotic behavior, in Lp (1 ≤ p ≤ ∞), of the derivatives Dγu(t) of the solution of the convection-diffusion equation...
On the continuity of heat potentials
On the iterated Green functions on a bounded domain and their related Kato class of potentials.
On the least principal fundamental solution of a parabolic differential equation
On the operator related to Bessel heat equation.
On the relative fundamental solutions for a second order differential operator on the Heisenberg group
Let Hₙ be the (2n+1)-dimensional Heisenberg group, let p,q ≥ 1 be integers satisfying p+q=n, and let , where X₁,Y₁,...,Xₙ,Yₙ,T denotes the standard basis of the Lie algebra of Hₙ. We compute explicitly a relative fundamental solution for L.
Operator equations, separation of variables and relativistic alterations.
Optimal -properties of Green’s functions for non-divergence elliptic equations in two dimensions
A sharp integrability result for non-negative adjoint solutions to planar non-divergence elliptic equations is proved. A uniform estimate is also given for the Green's function.