A class of De Giorgi type and local boundedness

Duchao Liu, Jinghua Yao

DOI: http://dx.doi.org/10.12775/TMNA.2017.063


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.


Musielak-Sobolev space; local bounded property

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