Chapter 16.5, Problem 35E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Recall from Section 14.3 that a function *g* is called *harmonic* on *D* if it satisfies Laplace’s equation, that is, ∇^{2}*g* = 0 on *D*. Use Green’s first identity (with the same hypotheses as in Exercise 33) to show that if *g* is harmonic on *D*, then
*D _{n} g* is the normal derivative of

To determine

**To show:** The

Explanation

Consider the expression of second vector form of Greenâ€™s Theorem.

As the

Rearrange the equation.

Consider

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