@article{Liu2024, 
author = {Jiayin Liu and Jun Zheng},
title = {Boundedness and higher integrability of minimizers to a class of two-phase free boundary problems under non-standard growth conditions},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {18574-18588},
keywords = {free boundary problem, two-phase, integrability, non-standard growth, minimizer},
url = {https://www.sciopen.com/article/10.3934/math.2024904},
doi = {10.3934/math.2024904},
abstract = {In this paper, we are concerned with the existence, boundedness, and integrability of minimizers of heterogeneous, two-phase free boundary problems              J              γ        (  u  )  =      ∫          Ω            (          f      (      x      ,      ∇      u      )      +              λ                  +                    (              u                  +                            )                  γ                    +              λ                  −                    (              u                  −                            )                  γ                    +      g      u        )    d  x  →  min under non-standard growth conditions. Included in such problems are heterogeneous jets and cavities of Prandtl-Batchelor type with    γ  =  0, chemical reaction problems with    0  <  γ  <  1, and obstacle type problems with    γ  =  1, respectively.}
}