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arXiv · 1906.01866

Hölder continuity of $ω$-minimizers of functionals with generalized Orlicz growth

Petteri Harjulehto·Peter Hästö·Mikyoung Lee
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Abstract

We show local Hölder continuity of quasiminimizers of functionals with non-standard (Musielak--Orlicz) growth. Compared with previous results, we cover more general minimizing functionals and need fewer assumptions. We prove Harnack's inequality and a Morrey type estimate for quasiminimizers. Combining this with Ekeland's variational principle, we obtain local Hölder continuity for $ω$-minimizers.

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Petteri Harjulehto, Peter Hästö, Mikyoung Lee. 2022-08-08. Hölder continuity of $ω$-minimizers of functionals with generalized Orlicz growth. https://doi.org/10.2422/2036-2145.201908_015

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