@article{Zha2023, 
author = {Xicuo Zha and Shuibo Huang and Qiaoyu Tian},
title = {Uniform boundedness results of solutions to mixed local and nonlocal elliptic operator},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {9},
pages = {20665-20678},
keywords = {mixed local and nonlocal operator, bioundedness, Stampacchia method},
url = {https://www.sciopen.com/article/10.3934/math.20231053},
doi = {10.3934/math.20231053},
abstract = {In this paper, by the Stampacchia method, we consider the boundedness of positive solutions to the following mixed local and nonlocal quasilinear elliptic operator                                 {                                                    −                                  Δ                                      p                                                  u                +                (                −                Δ                                  )                                      p                                    s                                u                =                f                (                x                )                                  u                                      γ                                                  ,                                            x                ∈                Ω                ,                                                                    u                =                0                ,                                                                                                                                                                            x                ∈                                                      R                                                        N                                                  ∖                Ω                ,                                                                  where    s  ∈  (  0  ,  1  ),    1  <  p  <  N,    f  ∈      L          m        (  Ω  ) with    m  >            N      p              p      (      s      +      p      −      1      )      −      γ      (      N      −      s      p      )      ,    0  ⩽  γ  <      p    s    ∗    −  1,        p    s          ∗        =            N      p              N      −      s      p       is the critical Sobolev exponent.}
}