Partial Hölder continuity for discontinuous elliptic problems with VMO-coefficients

Bögelein V, Duzaar F, Habermann J, Scheven C (2011)

Publication Type: Journal article

Publication year: 2011

Journal

Publisher: London Mathematical Society

Book Volume: 103

Pages Range: 371-404

Journal Issue: 3

URI: http://plms.oxfordjournals.org/content/early/2011/02/27/plms.pdr009.abstract

DOI: 10.1112/plms/pdr009

Abstract

We establish partial Hölder continuity for vector-valued solutions u: Ω → ^N to elliptic systems of the type as well as for minimizers u: Ω → ^N of quasi-convex functionals where the structure function a, respectively, the integrand f is possibly discontinuous with respect to x. More precisely, we merely impose a uniform VMO-condition with respect to the x-dependence and continuity with respect to the u-dependence and prove Hölder continuity of the solutions, respectively, the minimizers outside of a negligible set. 2011 London Mathematical Society2011 © 2011 London Mathematical Society.

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APA:

Bögelein, V., Duzaar, F., Habermann, J., & Scheven, C. (2011). Partial Hölder continuity for discontinuous elliptic problems with VMO-coefficients. Proceedings of the London Mathematical Society, 103(3), 371-404. https://dx.doi.org/10.1112/plms/pdr009

MLA:

Bögelein, Verena, et al. "Partial Hölder continuity for discontinuous elliptic problems with VMO-coefficients." Proceedings of the London Mathematical Society 103.3 (2011): 371-404.

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