Partial Regularity for BV Minimizers

By Franz Gmeineder, Jan Kristensen. Archive for Rational Mechanics and Analysis, 2018

53 citations recorded by the source corpus.

We establish an $${\varepsilon}$$ε-regularity result for the derivative of a map of bounded variation that minimizes a strongly quasiconvex variational integral of linear growth, and, as a consequence, the partial regularity of such BV minimizers. This result extends the regularity theory for minimizers of quasiconvex integrals on Sobolev spaces to the context of maps of bounded variation. Previous partial regularity results for BV minimizers in the linear growth set-up were confined to the convex situation.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f436143ab7b3e23743f7534df987b1cb933a2897

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In Applied Mathematics

1. Cristiana De Filippis
2. Giuseppe Mingione
3. Vicentiu D. Rădulescu
4. Patrick Winkert
5. Frank Duzaar
6. Paolo Baroni
7. Verena Bogelein
8. Jan Kristensen

In Computational Theory and Mathematics

1. Cristiana De Filippis
2. Giuseppe Mingione
3. Patrick Winkert
4. Vicentiu D. Rădulescu
5. Frank Duzaar
6. Jan Kristensen
7. Verena Bogelein
8. Paolo Baroni

In Geometry and Topology

1. Cristiana De Filippis
2. Giuseppe Mingione
3. Thomas Schmidt
4. Frank Duzaar

Citations in the corpus

• On the Regularity of Minima of Non-autonomous Functionals (2019, background): “7) involves a suitable use of relaxed functionals and spaces of BV functions [6,9,27,28].”