We consider the mixed local and nonlocal functionals with nonstandard growth with , , and being a bounded domain. We study, utilizing expansion of positivity, local behavior of the minimizers of such problems, involving local boundedness, local Hölder continuity, and Harnack inequality. This solves a problem raised by De Filippis and Mingione [Math. Ann. 388 (2024) 262–328].
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Ding et al. (2024) studied this question.
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