As far as I can see the JVM reserves for each field the requiered memory for one instance of MyObject so a lot of memory is reserved even though it is never really used.
No, it doesn't. It reserves enough memory for 100 object references, not 100 instances of MyObject. An object reference is not big (32 or 64 bits, see this answer for details). ASCII-art below.
Now, if you're bothered by even reserving 100 slots that are the size of an int or long, you could use ArrayList which will reallocate a backing array as necessary (but this can add to memory fragmentation), a LinkedList which doesn't use an array at all (but has higher memory overhead for the entries that it does have), or even a structure such as a Map that doesn't (necessarily) use arrays at all (but again has higher overhead per entry).
ASCII-art and details for the 100-place array:
So when you first create that array, here's what you have in memory:
+-----------+
| arr |
+-----------+ +------------+
| reference |------>| MyObject[] |
+-----------+ +------------+
| null |
| null |
| null |
| (96 more) |
| null |
+------------+
Then you assign an instance, say:
arr[1] = new MyObject();
That gives you
+-----------+
| arr |
+-----------+ +------------+
| reference |------>| MyObject[] |
+-----------+ +------------+
| null | +-------------------+
| reference |---->| MyObject instance |
| null | +-------------------+
| (96 more) | | someField |
| null | | someOtherField |
+------------+ | ... |
+-------------------+
...then maybe you add another:
+-----------+
| arr |
+-----------+ +------------+
| reference |------>| MyObject[] |
+-----------+ +------------+
| null | +-------------------+
| reference |---->| MyObject instance |
| reference |--+ +-------------------+
| (96 more) | | | someField |
| null | | | someOtherField |
+------------+ | | ... |
| +-------------------+
|
| +-------------------+
+->| MyObject instance |
+-------------------+
| someField |
| someOtherField |
| ... |
+-------------------+
...and so on as you store more instances in the array.