Title

Residue Type Phenomenon for the Fundamental Solution of Laplacian and its Applications

Document Type

Presentation

Presentation Date

Summer 6-12-2013

Conference Name

Computational Methods and Function Theory (CMFT 2013)

Conference Location

Shantou, Guangdon, China

Abstract

In this talk, we discover a Residue type phenomenon for the fundamental solution of Laplacian in Rn, n ≥ 3. This is analogous to the Residue theorem for the Cauchy kernel in C. With the aid of the Residue type formula, we derive the higher order derivative formula for the Newtonian potential and obtain its appropriate Ck, a estimates. Those estimates allow us to obtain the existence of solutions to higher order Poisson type nonlinear systems making use of the fixed point theorem.

Disciplines

Analysis | Harmonic Analysis and Representation

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