@article{Zhang2023, 
author = {Bei-Lei Zhang and Bin Ge},
title = {Gradient estimates for the double phase problems in the whole space},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {12},
pages = {7349-7364},
keywords = {regularity, gradient, double phase, Calderón-Zygmund estimate, non-uniform ellipticity},
url = {https://www.sciopen.com/article/10.3934/era.2023372},
doi = {10.3934/era.2023372},
abstract = {This paper presents Calderón-Zygmund estimates for the weak solutions of a class of nonuniformly elliptic equations in              R        n  , which are obtained through the use of the iteration-covering method. More precisely, a global Calderón-Zygmund type result         |    f            |                      p        1              +  a  (  x  )      |    f            |                      p        2              ∈      L    s    (            R        n    )  ⇒      |    D  u            |                      p        1              +  a  (  x  )      |    D  u            |                      p        2              ∈      L    s    (            R        n    )        f    o    r        a    n    y      s  >  1is established for the weak solutions of     −      d    i    v    A  (  x  ,  D  u  )  =  −      d    i    v    F  (  x  ,  f  )        i    n                R        n    ,which are modeled on     −      d    i    v    (      |    D  u            |                      p        1            −      2        D  u  +  a  (  x  )      |    D  u            |                      p        2            −      2        D  u  )  =  −      d    i    v    (      |    f            |                      p        1            −      2        f  +  a  (  x  )      |    f            |                      p        2            −      2        f  )  ,where    0  ≤  a  (  ⋅  )  ∈      C          0      ,      α        (            R        n    )  ,    α  ∈  (  0  ,  1  ] and    1  <      p    1    <      p    2    <      p    1    +            α              p        1              n  .}
}