Intraperitoneal Bortezomib and Carboplatin in Treating Patients With Persistent or Recurrent Ovarian Epithelial Cancer, Fallopian Tube Cancer, or Primary Peritoneal Cancer

Inclusion Criteria: * Patients must have recurrent or persistent epithelial ovarian, fallopian tube, or primary peritoneal cancer; histologic documentation of the original primary tumor is required via the pathology report * Patients with the following histologic epithelial cell types are eligible: serous adenocarcinoma, endometrioid adenocarcinoma, mucinous adenocarcinoma, undifferentiated carcinoma, clear cell adenocarcinoma, mixed epithelial carcinoma, transitional cell carcinoma, malignant Brenner's tumor, or adenocarcinoma not otherwise specified (N.O.S) * Patients must have either measurable disease or detectable disease: * Measurable disease will be defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1; measureable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest dimension to be recorded); each lesion must be \>= 10 mm when measured by computed tomography (CT), magnetic resonance imaging (MRI) or caliper measurement by clinical exam; or \>= 20 mm when measured by chest x-ray; lymph nodes must be \>= 15 mm in short axis when measured by CT or MRI * Detectable disease is defined in a patient as one who does not have measurable disease but has at least one of the following conditions: * Baseline values of cancer antigen (CA)-125 at least twice the upper limit of normal * Ascites and/or pleural effusion attributed to tumor * Solid and/or cystic abnormalities on radiographic ima…