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

• Petteri Harjulehto ^[1] ; Peter Hästo ^[1] ; Mikyoung Lee ^[2]
  1. [1] University of Turku

     University of Turku

     Turku, Finlandia

     
  2. [2] Pusan National University

     Pusan National University

     Corea del Sur

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 22, Nº 2, 2021, págs. 549-582
• Idioma: inglés
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• Resumen

  • We show local H ̈older continuity of quasiminimizers of function- als with non-standard (Musielak–Orlicz) growth. Compared with previous re- sults, 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 H ̈older con- tinuity for !-minimizers.