If you used the jedit installer to install it, it should have created a file in your home bin directory, that is, if your username is "user":
/home/user/bin/jedit
and so you can safely edit it and change all the variables you need

i used ./configure make and make install commands to install the software. I dont have the following directory /home/user/bin/jedit but i do have /home/steve/.jedit there are files and subfolders in there but i cant find anything regarding JAVA_HOME. I have one other file jedit that is located in /usr/bin. This seems more promising but i get it to work with any modification. The file reads as follows:

#!/bin/sh
#
# Runs jEdit - Programmer's Text Editor.
#

# Set jvm heap initial and maximum sizes (in megabytes).
JAVA_HEAP_INIT_SIZE=64
JAVA_HEAP_MAX_SIZE=192

# Find a java installation.
if [ -z "$JAVA_HOME" ]; then
echo "Warning: \$JAVA_HOME environment variable not set! Consider setting it."
echo " Attempting to locate java..."
j=`which java 2>/dev/null`
if [ -z "$j" ]; then
echo "Failed to locate the java virtual machine! Bailing..."
exit 1
else
echo "Found a virtual machine at: $j..."
JAVA="$j"
fi
else
JAVA="$JAVA_HOME/bin/java"
# Various attempts at editing the file
# 1
# export JAVA_HOME=/usr/lib/jvm/java-1.5.0-sun-1.5.0.08
# export PATH=$JAVA_HOME/bin:$PATH
# 2
# JAVA="$JAVA_HOME/usr/lib/jvm/java-1.5.0-sun-1.5.0.08"
# End editing attempts
fi

# Launch application.
exec $JAVA -Xms${JAVA_HEAP_INIT_SIZE}M -Xmx${JAVA_HEAP_MAX_SIZE}M -jar /usr/share/jEdit/jedit.jar -reuseview $@