Under appropriate assumptions on the $N(\Omega)$-function, the De Giorgi process is presented in the framework of Musielak-Orlicz-Sobolev spaces. As the applications, the local boundedness property of the minimizers for a class of the energy functionals in Musielak-Orlicz-Sobolev spaces is proved; and furthermore, the local boundedness of the weak solutions for a class of fully nonlinear elliptic equations is provided.
"A class of De Giorgi type and local boundedness." Topol. Methods Nonlinear Anal. 51 (2) 345 - 370, 2018. https://doi.org/10.12775/TMNA.2017.063