Imatinib Mesylate in Treating Patients With Stage III or Stage IV Ovarian Epithelial or Primary Peritoneal Cancer

Inclusion Criteria: * Histologically confirmed epithelial carcinoma of the ovary or primary peritoneal serous papillary carcinoma * No mixed Mullerian tumors * No borderline ovarian tumors * Stage III or IV disease at time of diagnosis by surgical staging * Expression of KIT (CD117) and/or platelet-derived growth factor receptor by immunohistochemistry * Relapsed within 6 months after completion of or progressed while receiving prior frontline chemotherapy with a platinum (cisplatin or carboplatin) and a taxane(paclitaxel or docetaxel) administered concurrently or sequentially * Measurable disease * Performance status - Zubrod 0-1 * Absolute neutrophil count at least 1,500/mm\^3 * Platelet count at least 100,000/mm\^3 * Hemoglobin at least 9 g/dL (transfusion allowed) * Bilirubin no greater than 1.5 times upper limit of normal (ULN) * SGOT or SGPT no greater than 2.5 times ULN * Creatinine no greater than 1.5 times ULN * No New York Heart Association class III or IV heart disease (e.g., congestive heart failure or myocardial infarction within the past 2 months) * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective barrier contraception during and for 3 months after study participation * No other malignancy within the past 5 years except adequately treated basal cell or squamous cell skin cancer, carcinoma in situ of the cervix, or other adequately treated stage I or II cancer in complete remission * At least 28 days since prior biologic therapy * No concurrent anticancer biologic therapy * No concurrent cytokines (e.g., filgrastim \[G-CSF\] or sargramostim \[GM-CSF\]) * At least 28 days since prior chemotherapy * No more than 3 prior chemotherapy regimens in addition to frontline chemotherapy * Retreatment with a platinum agent or with the same taxane as in the frontline regimen is not counted as an additional regimen * No concurrent chemotherapy * Prior hormonal therapy allowed * Recovered from prior radiotherapy * No prior radiotherapy to more than 25% of bone marrow * No concurrent radiotherapy * Prior surgical debulking allowed for relapsed disease if measurable disease remains after surgery * At least 14 days since prior major surgery * Recovered from all prior surgery * At least 28 days since prior investigational drugs * No concurrent therapeutic doses of warfarin for anticoagulation (heparin or mini-dose warfarin (1 mg/day) allowed) * No other concurrent anticancer agents * No other concurrent investigational drugs