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On the Dirichlet problem for variational integrals in BV by Lisa Beck; Thomas Schmidt is a Mathematics article available to read on EtoBox.

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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 1⁄4 1-where the problem coincides with the non-parametric least area problem-to the general vectorial setting N A N. 6. Non-uniqueness and boundary behavior A. (Semi-)Continuity and existence B. Additional remarks on the Dirichlet problem C. Non-

Who reads On the Dirichlet problem for variational integrals in BV?

Author

Lisa Beck; Thomas Schmidt

Publisher

Walter de Gruyter GmbH

Published

2013

Language

EN

Field

Mathematics (Physical Sciences)