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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.

Mokhtar Kirane, Mahmoud Qafsaoui (2002)

Revista Matemática Complutense

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

Miroslav Dont (1981)

Časopis pro pěstování matematiky

On the iterated Green functions on a bounded domain and their related Kato class of potentials.

Mâagli, Habib, Zeddini, Noureddine (2007)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On the least principal fundamental solution of a parabolic differential equation

A. Wójcik (1980)

Annales Polonici Mathematici

On the operator $\oplus_{B}^{k}$ related to Bessel heat equation.

Satsanit, Wanchak (2010)

Mathematical Problems in Engineering

On the relative fundamental solutions for a second order differential operator on the Heisenberg group

T. Godoy, L. Saal (2001)

Studia Mathematica

Let Hₙ be the (2n+1)-dimensional Heisenberg group, let p,q ≥ 1 be integers satisfying p+q=n, and let $L = \sum_{j = 1}^{p} (X ²_{j} + Y ²_{j}) - \sum_{j = p + 1}^{n} (X ²_{j} + Y ²_{j})$ , 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.

Hermann, Robert A. (1995)

International Journal of Mathematics and Mathematical Sciences

Optimal $L^{p}$ -properties of Green’s functions for non-divergence elliptic equations in two dimensions

Gioconda Moscariello, Carlo Sbordone (2005)

Studia Mathematica

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.

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