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