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ISSN 1947-6221(e) ISSN 0065-9266(p)

On first and second order planar elliptic equations with degeneracies

Author: Abdelhamid Meziani
Journal: Memoirs of the AMS 217 (2012)
MSC (2000): Primary 35J70, 35F05, 30G20
Posted: May 18, 2011
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Abstract: 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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