Partial regularity of minimizers of quasiconvex variational integrals via interpolation

Partial regularity of minimizers of quasiconvex variational integrals via interpolation

We prove optimal partial regularity of vector-valued minimizers u of the quasiconvex variational integral ∫F(x,u,Du)dx under polynomial growth of its integrand F. We employ a new direct method based on the interpolation of a Sobolev function w between its gradient Dw and the elliptic operator divADw...

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Veröffentlicht in:Journal of mathematical analysis and applications 2025-05, Vol.545 (2), p.129161, Article 129161
1. Verfasser: Hamburger, Christoph
Format: Artikel
Sprache:eng
Schlagworte:
Calculus of variations
Interpolation inequality
Minimizer
Partial regularity
Quasiconvexity
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Zusammenfassung:We prove optimal partial regularity of vector-valued minimizers u of the quasiconvex variational integral ∫F(x,u,Du)dx under polynomial growth of its integrand F. We employ a new direct method based on the interpolation of a Sobolev function w between its gradient Dw and the elliptic operator divADw with constant coefficient A.
ISSN:0022-247X
DOI:10.1016/j.jmaa.2024.129161