This is an open-label, non-randomized, dose escalation study. Patients will be treated with lenvatinib once daily. Each four-week treatment period will be considered to be one treatment cycle. The selection of subsequent dose levels will be performed according to an accelerated design: Although initially 3 patients per dose level will be entered, the next dose level can be opened for patient accrual after only the first patient in the previous cohort completes Cycle 1 with no drug-related toxicity greater than grade 1 (except alopecia, lymphopenia and anemia).