The study demonstrates the relaxation of a quasi-convex functional with variable exponent growth, indicating significant findings in bounded variation spaces.
We prove a relaxation result for a quasi-convex bulk integral functional with variable exponent growth in a suitable space of bounded variation type. A key tool is a decomposition under mild assumptions of the energy into absolutely continuous and singular parts weighted via a recession function.
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Bertazzoni et al. (2025) studied this question.
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