Here you could do something like: 
```
{"query": {"filtered": {
    "filter": {"terms": {"user_id": matching_user_ids},
    "query": {"fuzzy_like_this_field": {
        "name.exact": case_search
    }}
}}}
```
or whatever type of query makes the most sense for that text matching in this use case.  http://www.elasticsearch.org/guide/en/elasticsearch/reference/1.x/query-dsl-flt-field-query.html