Fundamental solutions of homogeneous elliptic differential operators

FUNDAMENTAL SOLUTIONS OF PSEUDO-DIFFERENTIAL OPERATORS OVER p−ADIC FIELDS

We show the existence of fundamental solutions for p−adic pseudodifferential operators with polynomial symbols.

Fundamental Solutions: Ii-matrix Operators

In this tutorial, we will continue the discussion, started in the tutorial 4, about the derivation of the fundamental solutions. In the former tutorial, we presented techniques for setting up the fundamental solution for simple and compound operators. Herein, we will discuss the use of operator decoupling technique to breakdown matrix operators to simple or compound scalar ones. This method is ...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

On the fundamental solutions of a class of elliptic quartic operators in dimension 3

The (uniquely determined) even and homogeneous fundamental solutions of the linear elliptic partial differential operators with constant coefficients of the form ∑3 j=1 ∑3 k=1 cjk∂ j ∂2 k are represented by elliptic integrals of the first kind. Thereby we generalize Fredholm’s example ∂4 1 +∂4 2 +∂4 3 , which, up to now, was the only irreducible homogeneous quartic operator in 3 variables the f...

Fundamental Solutions of Cubic Operators In