A uniqueness result for graphs of least gradient

2 November 2009
We investigate the minimization problem for the variational integral $$\int_\Omega\sqrt{1+|Dw|^2}\,dx$$ in Dirichlet classes of vector-valued functions $w$. It is well known that the existence of minimizers can be established if the problem is formulated in a generalized way in the space of functions of bounded variation. In this talk we will discuss a uniqueness theorem for these generalized minimizers. Actually, the theorem holds for a larger class of variational integrals with linear growth and was obtained in collaboration with Lisa Beck (SNS Pisa).
  • Partial Differential Equations Seminar