## Tags » Maximum Principle

#### Newtonian Potential

— 1. Definition of Newtonian Potential —

895 more wordsDefinition 1 Let be a bounded open set, we define the Newtonian potential of is the function on by…

#### Behavior of harmonic functions comparing with a Green's function

Theorem Let , satisfies

If there exists such that

If as , then in .

*Proof:* Without loss of generality assume on , or we can add a large constant on to make it positive on boundary.