**— 1. Definition of Newtonian Potential —**

Definition 1Let be a bounded open set, we define the Newtonian potential of is the function on bywhere is the fundamental solution of Laplace’s equation.

Advertisements

Skip to content
# Tag: Perron’s method

# Newtonian Potential

# A Perron-type method

**— 1. Definition of Newtonian Potential —**

Definition 1Let be a bounded open set, we define the Newtonian potential of is the function on bywhere is the fundamental solution of Laplace’s equation.

Advertisements

I am now reviewing Perron’s method and it is a fun to go over a similar argument like this. The materials come from the lecture by Prof. Li and T.Aubin’s book.

TheoremOn a compact Riemannian manifold without boundary , the equationwith and on , has a solution .