Partial regularity for ω-minimizers of quasiconvex functionals

Journal article

Abstract:: We establish partial regularity for the ω-minimizers of quasiconvex functionals of power growth. A first-order partial regularity result of BV ω-minimizers is obtained in the linear growth case under a Dini-type condition on ω. Only assuming the smallness of ω near the origin, we show partial Hölder continuity in the subquadratic case by considering a normalised excess.

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Publisher:: Springer
Journal:: Calculus of Variations and Partial Differential Equations More from this journal
Volume:: 61
Issue:: 5
Article number:: 178
Publication date:: 2022-07-07
Acceptance date:: 2022-05-20
DOI:: 10.1007/s00526-022-02269-6
EISSN:: 1432-0835
ISSN:: 0944-2669

Copyright holder:: Li
Rights statement:: © The Author(s) 2022. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

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