I would create your date dimension with an integer key (clustered primary index) with the integer date value for that day. For example, today's key value would be 20160629. There are some date dimension build scripts out there in the internet if you search for them. Then, in your related tables, include the same integer date value for relating the tables. If you can't add this to the table, just add it into the table in SSAS by replacing your tblApplication with a named query in your data source view. You can use the existing date value in your table to derive the integer date value to link your tables in the DSV.

My preference would be to model this into your physical table though. That way, it's easier to query the data mart and get the same values as what your cube pulls up.