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On the Dirichlet problem for variational integrals in BV
-
Lisa Beck
and
Thomas Schmidt
Published/Copyright:
February 11, 2012
Abstract
We investigate the Dirichlet problem for multidimensional variational integrals with linear growth which is formulated in a generalized way in the space of functions of bounded variation. We prove uniqueness of minimizers up to additive constants and deduce additional assertions about these constants and the possible (non-)attainment of the boundary values. Moreover, we provide several related examples. In the case of the model integral
our results extend classical results from the scalar case N = 1—where the problem coincides with the non-parametric least area problem—to the general vectorial setting N ∈ ℕ.
Received: 2010-08-23
Revised: 2011-04-19
Published Online: 2012-02-11
Published in Print: 2013-01
©[2013] by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Potential automorphy for certain Galois representations to GL2n
- Ring completion of rig categories
- Géométrie birationnelle équivariante des grassmanniennes
- Uniformly effective boundedness of Shafarevich Conjecture-type
- On the Dirichlet problem for variational integrals in BV
- The pseudo-Calabi flow
