Solution Found!
Derive the three-dimensional maximum principle from the
Chapter 7, Problem 1(choose chapter or problem)
QUESTION:
Derive the three-dimensional maximum principle from the mean value property.
Questions & Answers
QUESTION:
Derive the three-dimensional maximum principle from the mean value property.
ANSWER:Step 1 of 2
The maximum principle says that, any solid region considered as a , is a non-constant harmonic function and it cannot take maximum value inside it but on bdy.
Let’s consider that is a non-constant harmonic function in it takes maximum value
inside .
According to the mean value property, we have
For all , then , for all since u is continuous and M is its Maximum.