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arXiv · 1711.11229

H\"{o}lder continuity for nonlinear elliptic problem in Musielak-Orlicz-Sobolev space

Beibei Wang·Duchao Liu·Peihao Zhao
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Abstract

Under appropriate assumptions on the $N(\Omega)$-fucntion, the De Giorgi process is presented in the framework of Musielak-Orlicz-Sobolev space to prove the H\"{o}lder continuity of fully nonlinear elliptic problems. As the applications, the H\"{o}lder continuity of the minimizers for a class of the energy functionals in Musielak-Orlicz-Sobolev spaces is proved; and furthermore, the H\"{o}lder continuity of the weak solutions for a class of fully nonlinear elliptic equations is provided.

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Beibei Wang, Duchao Liu, Peihao Zhao. 2017-11-30. H\"{o}lder continuity for nonlinear elliptic problem in Musielak-Orlicz-Sobolev space. https://arxiv.org/abs/1711.11229

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