We consider multidimensional variational integrals for vector-valued functions . Assuming that the integrand satisfies the standard smoothness, convexity and growth assumptions only near we investigate the partial regularity of minimizers (and generalized minimizers) . Introducing the open set we prove that is dense in , but we demonstrate for by an example that may have positive measure. In contrast, for one has .
Additionally, we establish analogous results for weak solutions of quasilinear elliptic systems.
@article{ASNSP_2009_5_8_3_469_0,
author = {Scheven, Christoph and Schmidt, Thomas},
title = {Asymptotically regular problems II: Partial Lipschitz continuity and a singular set of positive measure},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 8},
number = {3},
year = {2009},
pages = {469-507},
zbl = {1197.49043},
mrnumber = {2581424},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2009_5_8_3_469_0}
}
Scheven, Christoph; Schmidt, Thomas. Asymptotically regular problems II: Partial Lipschitz continuity and a singular set of positive measure. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 8 (2009) no. 3, pp. 469-507. http://www.numdam.org/item/ASNSP_2009_5_8_3_469_0/
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