Zofia Szmydt

Local existence and regularity of solutions of singular elliptic operators on manifolds with corner singularities

Abstract The local existence and regularity of solutions of singular elliptic operators on manifolds with corner singularities are studied by means of a perturbation technique based on the theory of multidimensional Mellin transformation developed in this paper. Relations with 2-microlocal regularity are established.

Special solutions of the equations Pu = 0, Pu = δ for invariant linear differential operators with polynomial coefficients

Explicit formulas are given for certain solutions of the equations Pu = δ and Pu = 0 with P being a differential operator with polynomial coefficients preserving the form ∑i = 1n xip − ∑i = 1m yiq for arbitrary even integers p, q. These formulas are a direct consequence of the invariance of P and depend only up to a constant factor upon the operator P.