Call of java.awt.Desktop.getDesktop().browse(URI) fails. It fails both when browser is already running and not running. Call stack:
java.io.IOException: Failed to show URI:http://www.sun.com
        at sun.awt.X11.XDesktopPeer.launch(XDesktopPeer.java:75)
        at sun.awt.X11.XDesktopPeer.browse(XDesktopPeer.java:64)
        at java.awt.Desktop.browse(Desktop.java:368)
        at BrowserTest.main(BrowserTest.java:15)

Simple test class:
import java.awt.Desktop;
import java.net.URI;

public class BrowserTest {

    public BrowserTest () {
    }

    public static void main(String[] args) {
        if (Desktop.getDesktop().isSupported(Desktop.Action.BROWSE)) {
            try {
                Desktop.getDesktop().browse(new URI("http://www.sun.com"));
            }
            catch (Exception e) {
                e.printStackTrace();
            }
        }
    }
}

The same happens with JDK 7 b24. Gnome, JDS release 3.

bash-3.00$ uname -a
SunOS dhcp-eprg06-20-81 5.10 Generic_125101-10 i86pc i386 i86pc