On the Dirichlet problem for variational integrals in BV

Beck L, Schmidt T (2013)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2013

Journal

Journal für die reine und angewandte Mathematik Walter de Gruyter

Publisher: Walter de Gruyter

Book Volume: 674

Pages Range: 113-194

URI: http://cvgmt.sns.it/paper/355/

DOI: 10.1515/crelle.2011.188

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 [equation presented] 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. © 2013 Walter de Gruyter Berlin-Boston.

Authors with CRIS profile

Thomas Schmidt Department Mathematik

Involved external institutions

Universität Augsburg DE Germany (DE)

How to cite

APA:

Beck, L., & Schmidt, T. (2013). On the Dirichlet problem for variational integrals in BV. Journal für die reine und angewandte Mathematik, 674, 113-194. https://doi.org/10.1515/crelle.2011.188

MLA:

Beck, Lisa, and Thomas Schmidt. "On the Dirichlet problem for variational integrals in BV." Journal für die reine und angewandte Mathematik 674 (2013): 113-194.

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