### Show Posts

This section allows you to view all posts made by this member. Note that you can only see posts made in areas you currently have access to.

### Messages - Chaojie Li

Pages: 1 [2]
16
##### HA8 / Re: Solution of Question 2
« on: March 19, 2015, 09:07:29 PM »
part c

17
##### HA8 / Re: Solution of Question 2
« on: March 19, 2015, 09:07:08 PM »
part b

18
##### HA8 / Solution of Question 2
« on: March 19, 2015, 09:06:43 PM »
Using the proof of mean value theorem prove that if $\Delta u\ge 0$ in $B(y,r)$ then

1.  $u(y)$ does not exceed the mean value of $u$ over the sphere $S(y,r)$ bounding this ball:

u(y)\le \frac{1}{\sigma_n r^{n-1}}\int_{S(y,r)} u\,dS.
\label{equ-H8.2}

2.  $u(y)$ does not exceed the mean value of $u$ over this ball $B(y,r)$:

u(y)\le \frac{1}{\omega_n   r^n}\int_{B(y,r)} u\,dV.
\label{equ-H8.3}

3.  Formulate similar statements for functions satisfying $\Delta u\le 0$ (in the next problem we refer to them as (a)' and (b)').

Definition

a.  Functions having property (a) (or (b) does not matter) of the  previous problem are called  subharmoni

b.  Functions having property (a)' (or (b)' does not matter) are called   superharmonic.

Well, so 9 pm is good to post solution right?

19
##### HA3 / Re: HA3 problem 3
« on: March 19, 2015, 10:03:55 AM »
this is c and d

20
##### HA3 / Re: HA3 problem 3
« on: March 19, 2015, 09:44:06 AM »
this is part b

21
##### HA3 / Re: HA3 problem 3
« on: March 19, 2015, 09:28:36 AM »
i just see nobody post yet.

Pages: 1 [2]