The district is named after two rivers : The Elbe river forms the western border with Saxony . The Schwarze Elster ( `` Black Elster '' ) is a tributary of the Elbe and runs through the district . The district is named after two rivers - the Elbe river forms the western border with Saxony , the Schwarze Elster ( `` Black Elster '' ) is a tributary of the Elbe and runs through the district .