Regularity of Minimizers in the Two-Phase Free Boundary Problems in Orlicz–Sobolev Spaces

  • Jun Zheng

    Southwest Jiaotong University, Chengdu, China
  • Binhua Feng

    Northwest Normal University, Lanzhou, China
  • Peihao Zhao

    Lanzhou University, China

Abstract

In this paper, we consider the optimization problem of minimizing in the class of functions with for a given function , where is the class of weakly differentiable functions with . The conditions on the function allow for a different behavior at and at . For , we prove that every minimizer of is -continuous.

Cite this article

Jun Zheng, Binhua Feng, Peihao Zhao, Regularity of Minimizers in the Two-Phase Free Boundary Problems in Orlicz–Sobolev Spaces. Z. Anal. Anwend. 36 (2017), no. 1, pp. 37–47

DOI 10.4171/ZAA/1578