A Long-term Study of Baricitinib (LY3009104) With Topical Corticosteroids in Adults With Moderate to Severe Atopic Dermatitis That Are Not Controlled With Cyclosporine or for Those Who Cannot Take Oral Cyclosporine Because it is Not Medically Advisable

Inclusion Criteria:

• Have been diagnosed with moderate to severe Atopic Eczema (Atopic Dermatitis) for atleast 12 months.

• Have had inadequate response to existing topical (applied to the skin) medicationswithin 6 months preceding screening.

• Are willing to discontinue certain treatments for eczema (such as systemic andtopical treatments during a washout period).

• Agree to use emollients daily.

• Have a medical contraindication to cyclosporine, or had intolerance and/orunacceptable toxicity or inadequate response to cyclosporine in the past.

Exclusion Criteria:

• Are currently experiencing or have a history of other concomitant skin conditions (e.g., psoriasis or lupus erythematosus), or a history of erythrodermic, refractory,or unstable skin disease that requires frequent hospitalizations and/or intravenoustreatment for skin infections.

• A history of eczema herpeticum within 12 months, and/or a history of 2 or moreepisodes of eczema herpeticum in the past.

• Participants who are currently experiencing a skin infection that requirestreatment, or are currently being treated, with topical or systemic antibiotics.

• Have any serious illness that is anticipated to require the use of systemiccorticosteroids or otherwise interfere with study participation or require activefrequent monitoring (e.g., unstable chronic asthma).

• Have been treated with the following therapies:

• Monoclonal antibody for less than 5 half-lives prior to randomization.

• Received prior treatment with any oral Janus kinase (JAK) inhibitor less than 4weeks prior to randomization.

• Received oral corticosteroids within 4 weeks prior to randomization orparenteral corticosteroids administered by intramuscular or intravenous (IV)injection within 2 weeks prior to study entry or within 6 weeks prior toplanned randomization or are anticipated to require parenteral injection ofcorticosteroids during the study.

• Have had an intra-articular corticosteroid injection within 2 weeks prior tostudy entry or within 6 weeks prior to planned randomization.

• Have high blood pressure characterized by a repeated systolic blood pressure >160millimeters of mercury (mm Hg) or diastolic blood pressure >100 mm Hg.

• Have had major surgery within the past eight weeks or are planning major surgeryduring the study.

• Have experienced any of the following within 12 weeks of screening: venousthromboembolic event (VTE), myocardial infarction (MI), unstable ischemic heartdisease, stroke, or New York Heart Association Stage III/IV heart failure.

• Have a history of recurrent (≥ 2) VTE or are considered at high risk of VTE asdeemed by the investigator.

• Have a history or presence of cardiovascular, respiratory, hepatic,gastrointestinal, endocrine, hematological, neurological, lymphoproliferativedisease or neuropsychiatric disorders or any other serious and/or unstable illness.

• Have a current or recent and/or clinically serious viral, bacterial, fungal, orparasitic infection including but not limited to herpes zoster, tuberculosis.

• Have specific laboratory abnormalities related to thyroid, renal and liver function,or blood cells.

• Have received certain treatments that are contraindicated.

• Pregnant or breastfeeding.