Representation of the solutions of a strongly degenerate first order elliptic system by generalized Laplace integrals

Author:

JURGAITIS Donatas

AMS Classification:

35J70, 35C15

Keywords:

elliptic system, degeneration of system order, family of particular solutions, formal solution, multidimensional Laplace integral, power series

Abstract:

In the paper, a system of four partial differential equations of the first order is considered whose order strongly degenerates in a hyperplane of the three-dimensional complex space. Families of particular solutions, holomorphic everywhere, except for the points from the degeneration manifold, are constructed. This families are represented by multidimensional generalized Laplace integrals.

Download paper:

Jurgaitis-07-pdf.pdf

Vol. 2 (10), 2007