Imatinib Mesylate in Treating Patients With Refractory or Relapsed Ovarian Epithelial, Fallopian Tube, or Primary Peritoneal Cancer, or Ovarian Low Malignant Potential Tumor

DISEASE CHARACTERISTICS: * Histologically confirmed ovarian epithelial, fallopian tube, or primary peritoneal cancer OR * Histologically confirmed ovarian low malignant potential tumor with invasive recurrence * Relapsed after and/or refractory to platinum- and taxane-based chemotherapy * Patients in first relapse after a disease-free interval of more than 1 year are eligible * Measurable disease outside prior radiation field * Availability of a sentinel lesion that is adequate for core biopsy through percutaneous biopsy or simple laparoscopic means * Patients with clinical evidence of CNS involvement (abnormal clinical examination) must have a negative CT scan with contrast or MRI of the brain * No large volume ascites or pleural effusion PATIENT CHARACTERISTICS: Age: * Not specified Performance status: * ECOG 0-2 Life expectancy: * Not specified Hematopoietic: * WBC at least 3,000/mm\^3 * Absolute neutrophil count greater than 1,500/mm\^3 * Hemoglobin at least 9.0 g/dL (independent of epoetin alfa or transfusion) * Platelet count at least 100,000/mm\^3 Hepatic: * Bilirubin no greater than 1.5 mg/dL * Transaminases no greater than 2.5 times upper limit of normal Renal: * Creatinine no greater than 1.5 mg/dL Cardiovascular: * No myocardial infarction or unstable dysrhythmia within the past 6 months * No congestive heart failure (CHF), including CHF that may be compensated with furosemide Other: * No other invasive malignancy within the past 5 years except noninvasive nonmelanoma skin cancer * No active infection * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective barrier contraception during and for 3 months after study completion * Concurrent residual, stable, grade 2 or lower peripheral neuropathy allowed at the discretion of the principal investigator (PI) PRIOR CONCURRENT THERAPY: Biologic therapy: * At least 4 weeks since prior signal transduction therapy Chemotherapy: * See Disease Characteristics * At least 4 weeks since prior chemotherapy (6 weeks for mitomycin or carboplatin) Endocrine therapy: * At least 4 weeks since prior hormonal therapy Radiotherapy: * See Disease Characteristics * At least 4 weeks since prior radiotherapy Surgery: * See Disease Characteristics Other: * Recovered from prior anticancer therapy * At least 1 week since prior antibiotics * No more than 4 prior anticancer regimens * No concurrent ketoconazole, itraconazole, erythromycin, or clarithromycin * No concurrent therapeutic warfarin * Patients who can be safely converted over to low molecular weight heparin are eligible * No concurrent grapefruit or grapefruit juice * No concurrent combination antiretroviral therapy for HIV-positive patients * No concurrent alternative or complementary therapies or over-the-counter agents unless approved by the PI * Concurrent medications that may alter the metabolism of imatinib mesylate and lead to potential toxicity are allowed at the discretion of the PI