Residue Type Phenomenon for the Fundamental Solution of Laplacian and its Applications
Computational Methods and Function Theory (CMFT 2013)
Shantou, Guangdon, China
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.
Analysis | Harmonic Analysis and Representation
Yuan Zhang and Yifei Pan (2013).
Residue Type Phenomenon for the Fundamental Solution of Laplacian and its Applications. Presented at Computational Methods and Function Theory (CMFT 2013), Shantou, Guangdon, China.