Not enough information to answer, we don't even know which libraries you use.
Also, have you information in the Java console?

sorry, I use only the core video library.

On win I don't have problems lauching the index.html file, the camera works.

On Linux I don't know where to seek for the console, but in the bottom bar of Firefox i read that the applet can't be initialized.

On Windows, you can activate the Java console from Firefox itself, or from the general Java settings.
Have you QuickTime installed in the Linux environment?

on windows I have the Java console activated but the message I have when I launch the jar is displayed on a basic sistem window and I don't have any tray icon of the console.

On linux I tried to install the QT but it doesn't seem to work, neither if I launch from the Processing enviroment!

So I tried to use JMyron, but the applet doesn't work at all!
When I launch the html I got this from the console:

Exception in thread "Animation Thread" java.lang.UnsatisfiedLinkError: no JMyron in java.library.path
    at java.lang.ClassLoader.loadLibrary(Unknown Source)
    at java.lang.Runtime.loadLibrary0(Unknown Source)
    at java.lang.System.loadLibrary(Unknown Source)
    at JMyron.JMyron.<clinit>(JMyron.java:14)
    at paintRGB_JMyron.setup(paintRGB_JMyron.java:85)
    at processing.core.PApplet.handleDraw(Unknown Source)
    at processing.core.PApplet.run(Unknown Source)
    at java.lang.Thread.run(Unknown Source)
java.lang.NullPointerException
    at paintRGB_JMyron.stop(paintRGB_JMyron.java:369)
    at sun.plugin2.applet.Plugin2Manager$AppletExecutionRunnable.run(Unknown Source)
    at java.lang.Thread.run(Unknown Source)