Hölder continuity of omega-minimizers of functionals with generalized Orlicz growth



: Harjulehto Petteri, Hästö Peter, Lee Mikyoung

Publisher: SCUOLA NORMALE SUPERIORE

: 2021

: Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze

: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE

: ANN SCUOLA NORM-SCI

: 22

: 2

: 549

: 582

: 34

: 0391-173X

DOI: https://doi.org/10.2422/2036-2145.201908_015

: https://arxiv.org/pdf/1906.01866.pdf


We show local Holder 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 Holder continuity for omega-minimizers.



Last updated on 2024-26-11 at 17:47