//get requiredfields for usergiven sObjects
List<String> sObjList = new List<String>{'Account','Contact'};

Schema.DescribeSObjectResult[] descResult = Schema.describeSObjects(sObjList);

Map<String, List<String>> objToRequiredFieldsMap = new Map<String, List<String>>();



for(Schema.DescribeSObjectResult dsr : descResult){

    List<String> requiredFields = new List<String>();

    //get required fields

    Map<String, Schema.SObjectField> fieldMap = dsr.fields.getMap();

    for(String str : fieldMap.keySet()){

        Schema.DescribeFieldResult f = fieldMap.get(str).getDescribe();

        if(!f.isNillable()){

            requiredFields.add(f.getName());

        }

    }

    objToRequiredFieldsMap.put(dsr.getName(), requiredFields);

}

System.debug(objToRequiredFieldsMap);