It is very critical to understand how to handle installation of Java related applications in App-V environment.
While some are of the view that the application should be installed along with Java in the same bubble while some say that the Java version installed on the base machine can be used.

Here is how you can do both of these in a proper way:

1) Java installed locally on the machine: If Java is locally installed on the machine and you capture the App-V application, then you will see a hard coded entry in the registry. This basically points the App-V application to look for Java in this local machine location. If you upgrade your Java version from say 1.6.21 to 1.6.24, then you do not need to worry, however, if you do a major upgrade from 1.6.21 to 1.7.xx then you need to upgrade your App-V Application as well. You need to maintain the software library for all these applications and then upgrade them as part of Java Upgrade in the organization.

2) Java is installed as local copy inside App-V bubble: Java can also be installed as a local copy with your App-V application. There can be various reasons for doing this:
 a) Application is compatible only with a certain version of Java
 b) Application uses a higher version which is not locally installed.
 c) If Software manager do not want to upgrade the application every time Java gets updated.

In these cases a private copy of Java can be captured with App-V. However, there is a procedure for achieving this.
These steps will be helpful in doing this:

http://packagingguide.blogspot.com.au/2011/11/app-v-for-java-runtime-environment.html