Lower semicontinuity for functionals defined on piecewise rigid functions and on GSBD

Friedrich M, Perugini M, Solombrino F (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Journal of Functional Analysis Elsevier

Book Volume: 280

Article Number: 108929

Journal Issue: 7

DOI: 10.1016/j.jfa.2021.108929

Abstract

In this work, we provide a characterization result for lower semicontinuity of surface energies defined on piecewise rigid functions, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component is a skew symmetric matrix. This characterization is achieved by means of an integral condition, called BD-ellipticity, which is in the spirit of BV-ellipticity defined by Ambrosio and Braides [5]. By specific examples we show that this novel concept is in fact stronger compared to its BV analog. We further provide a sufficient condition implying BD-ellipticity which we call symmetric joint convexity. This notion can be checked explicitly for certain classes of surface energies which are relevant for applications, e.g., for variational fracture models. Finally, we give a direct proof that surface energies with symmetric jointly convex integrands are lower semicontinuous also on the larger space of GSBDp functions.

Authors with CRIS profile

Manuel Friedrich

Involved external institutions

Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE) Università degli Studi di Napoli Federico II IT Italy (IT)

How to cite

APA:

Friedrich, M., Perugini, M., & Solombrino, F. (2021). Lower semicontinuity for functionals defined on piecewise rigid functions and on GSBD. Journal of Functional Analysis, 280(7). https://dx.doi.org/10.1016/j.jfa.2021.108929

MLA:

Friedrich, Manuel, Matteo Perugini, and Francesco Solombrino. "Lower semicontinuity for functionals defined on piecewise rigid functions and on GSBD." Journal of Functional Analysis 280.7 (2021).

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