Purchase Solution

Harmonic Function: Analyticity, Compactness and Minimum Value

Not what you're looking for?

Ask Custom Question

Let (attached) be a function that is analytic and not constant throughtout a bounded domain (attached) and continuous (attached) on its boundary (here domain is an open connected set).
Prove, by considering (attached) , that the component function (attached) has a minimum value in the compact region (attached) which occurs on (attached) and never in (attached).

Use this result to formulate and prove a minimum principle for harmonic functions.

Please see the attached file for the fully formatted problems.

Purchase this Solution

Solution Summary

Harmonic Functions, Analyticity, Compactness and Minimum Value are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

Purchase this Solution


Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts