On First and Second Order Planar Elliptic Equations with Degeneracies

Details On First and Second Order Planar Elliptic Equations with Degeneracies On First and Second Order Planar Elliptic Equations with Degeneracies

2009-10-03

arxiv.org/abs/0910.0539v1

Mathematics

Analysis of PDEs

74 pages

Scientific paper

This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed. Properties of solutions, in a neighborhood of the degeneracy curve, are obtained through integral and series representations. An application to a second order elliptic equation with a punctual singularity is given.

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