A class of De Giorgi type and local boundedness - Liu, Duchao; Yao, Jinghua (Topological Methods in Nonlinear Analysis, 2018)
Under appropriate assumptions on the N(Ω)-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.