Actually, Israel does control the border with Egypt.

"Following the disengagement, Israel withdrew its forces from the southern border between Gaza and Egypt. At first, many thought that this brought an end to Israel's control of the border crossing between Gaza and Egypt, known as Rafah Crossing, which is now the only border crossing in the Gaza Strip that is not subject direct Israeli control. However, as time passed, it became clear that Israel retained the power to open and close the crossing at will, and since Hamas's takeover of the Palestinian security forces in Gaza, in June 2007, it has been almost permanently closed"

http://www.btselem.org/english/Gaza_Strip/Rafah_Crossing.asp

The people who are trying to bring humanitarian aid into Gaza at this time are saying that Israel is allowing a very small trickle to enter, but that most of the supplies are piling up at the wall outside of Gaza, and that the amount that is getting in is not anywhere near enough to prevent a humanitarian catastrophe.

http://www.arabicnews.com/ansub/Daily/Day/090128/2009012804.html