# (Non-)uniqueness of graphs of least gradient - theory and examples

## Venerdi' 2 dicembre 2011 - Lisa Beck

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Venerdi' 2 dicembre 2011 alle ore 11:00 in aula 2BC30, Lisa Beck (Hausdorff Center For Mathematics, Bonn) terra' un seminario dal titolo "(Non-)uniqueness of graphs of least gradient - theory and examples".

-Abstract
In this talk we will address some characteristics of minimization problems concerning variational integrals of linear growth. As a model case we study the minimization of the integral $$int_{Omega} sqrt{1 + |Dw|^2} dx$$ in Dirichlet classes of (vector-valued) function w. We first give some heuristics on existence and uniqueness (up to additive constants) of generalized minimizers. We then provide several classical examples (from the scalar case, i.e. from the non-parametric least area problem) and we investigate in more detail the phenomenon of non-uniqueness, which is closely related to the possible non-attainment of the boundary values.

Rif. int. M. Bardi, C. Marchi, D. Vittone