A Clinical Trial of BMX-010 in Adult Subjects With Atopic Dermatitis

Inclusion Criteria: * Male or female, at least 18 years of age at the time of consent; * Diagnosis of AD, as defined by the criteria of Hanifin and Rajka, stable in the last 4 weeks, with onset at least 6 months prior to screening (information obtained from medical chart or subject's physician, or directly from the subject). * Group 1 only: Subjects should have AD covering approximately 2-5% of the BSA at screening and Day 1 (excluding scalp, face, palms, soles, genitals, and folds). Subjects will treat approximately 5% of their BSA (excluding scalp, face palms, soles, genitals, and folds). * Group 2 only: 4. Group 2 only: Subject has active AD lesions covering 2-25% of the BSA at screening and Day 1 (excluding scalp, face, palms, soles, genitals, and folds from BSA calculation). * EASI score \>/= 5 (greater than or equal to 5) at screening and Day 1. * vIGA-AD score ≥ 2 (greater than or equal to 2) at screening and Day 1. * Candidate for topical treatment of AD; * Subjects must be willing to apply an emollient of their choice during study. * Females of child-bearing potential must have a negative urine pregnancy test at screening and on the day of the first drug administration; * Females of child-bearing potential must be willing to use 2 methods of contraception deemed adequate through the trial and for 1 month thereafter to be eligible for, and continue participation in, the study. * Ability to complete the study in compliance with the protocol, including agreement in writing to apply IP only to the assigned areas. * Ability to understand and provide written informed consent. Exclusion Criteria: * Subjects with AD only located on the hands and feet. * Subjects with clinically infected AD. * Subjects for which systemic pharmacotherapy or phototherapy for the treatment of AD is indicated or required. * Treatment with systemic retinoids, corticosteroids, immunomodulators or immunosuppressive agents (e.g., methotrexate, cyclosporine), cytotoxic agents, interferon, upadacitinib, abrocitinib, or baricitinib within 4 weeks of the Baseline visit or anticipated need for any of these therapies during the study period. * Treatment with topical corticosteroids, crisaborole, ruxolitinib, Vitamin D analogs, keratolytics, coal tar, calcineurin inhibitors, antihistamines or any other therapeutic agents besides bland emollients within 2 weeks of the Baseline visit or anticipated need for any of these. * Treatment with a biological agent (such as a monoclonal antibody) within a period of time of 12 weeks or 5 half-lives (whichever is longer) prior to Day 1. * Subject has used systemic antibiotics within 2 weeks or topical antibiotics within 1 week prior to Day 1. Of note, subjects with herpes labialis or genitalis and use of antivirals for these diseases are allowed. * Subject has used dupilumab within 26 weeks prior to Day 1. * Subject has used doxepin within 1 week prior to Day 1. * Subject has used hydroxyzine or diphenhydramine within 1 week prior to Day 1. * Subject has used topical products containing urea within 1 week prior to Day 1. * Subject has used medical devices, and bleach baths within 2 weeks prior to Day 1. * Subject has had excessive sun exposure, is planning a trip to a sunny climate, or has used tanning booths within 4 weeks prior to Day 1 or is not willing to minimize natural and artificial sunlight exposure during the study. Use of sunscreen products (except on treated lesions) and protective apparel are recommended when sun exposure cannot be avoided. * Subject has received an intravenous immunoglobulin (IVIg) therapy within 12 weeks prior to Day 1. * AD triggered by an unavoidable environmental allergen or irritant. * Contact dermatitis or drug-induced skin reactions. * Concomitant skin disease that could confound clinical evaluations or increase risk to the subject. * Systemic or skin infection requiring antimicrobial therapy within 14 days prior to Baseline. * Systemic chemotherapy or radiotherapy within 4 weeks of the Baseline Visit. * Immunocompromise of any cause, known human immunodeficiency virus infection, or acquired immunodeficiency syndrome, including patients receiving immune therapy. * Pregnancy, planned pregnancy, lactation, or inadequate contraception as judged by the investigator. * Active drug or alcohol dependence. * Significant acute or chronic medical, neurological, or psychiatric illness that, in the judgment of the investigator, could compromise subject safety, limit the subject's ability to complete the study, and/or compromise the objectives of the study; clinically significant renal or hepatic insufficiency. * History of malignancy, unless clinically cured for more than 5 years prior to Baseline. This exclusion does not apply to basal and squamous cell carcinomas of skin and carcinoma in situ of the cervix if they have been adequately treated and are clinically judged to be cured. * Subject had a major surgery within 8 weeks prior to Day 1 or has a major surgery planned during the study. * Participation in another investigational drug or vaccine trial concurrently or within 4 weeks for nonbiological investigational products or devices or 12 weeks (or 5 half-lives) for biological investigational products prior to Screening visit.