#### Question Details

##### (Solution) - Let E be a set in Rm For each u

Brief item decscription

Solution download

Item details:

Let E be a set in Rm. For each u: E ? R which has second-order partial derivatives on E, Laplace's equation is defined by

a) Show that if u is C2 on E, then ?u =  ? (u) on E.
b) Show that if E ? R3 satisfies the hypotheses of the Divergence Theorem, then
for all C2 functions u, v : E ? R.
c) Show that if E ? R3 satisfies the hypotheses of the Divergence Theorem, then
for all C2 functions u, v: E ? R.
d) A function u: E ? R is said to be harmonic on E if and only if u is C2 on E and ?u(x) = 0 for all x ? E. Suppose that E is a nonempty open region in R3 which satisfies the hypotheses of the Divergence Theorem. If u is harmonic on E, u is continuous on , and u = 0 on ?E, prove that u = 0 on .
e) Suppose that V is open and nonempty in R2, that u is C2 on V, and that u is continuous on . Prove that u is harmonic on V if and only if
for all two-dimensional regions E ? V which satisfy the hypotheses of Green's Theorem.

About this question:
STATUS
Answered
QUALITY
Approved
ANSWER RATING

This question was answered on: Jul 11, 2017

Solution~000910112952.zip (18.37 KB)

Buy this answer for only: \$15

Pay using PayPal (No PayPal account Required) or your credit card. All your purchases are securely protected by PayPal.

### Need a similar solution fast, written anew from scratch? Place your own custom order

We have top-notch tutors who can help you with your essay at a reasonable cost and then you can simply use that essay as a template to build your own arguments. This we believe is a better way of understanding a problem and makes use of the efficiency of time of the student. New solution orders are original solutions and precise to your writing instruction requirements. Place a New Order using the button below.

v>