@article{Lee2025, 
author = {Ho-Sik Lee and Youchan Kim},
title = {Boundary Riesz potential estimates for parabolic equations with measurable nonlinearities},
year = {2025},
journal = {Communications in Analysis and Mechanics},
volume = {17},
number = {1},
pages = {61-99},
keywords = {nonlinear parabolic equations, Riesz potentials, measurable nonlinearities},
url = {https://www.sciopen.com/article/10.3934/cam.2025004},
doi = {10.3934/cam.2025004},
abstract = {We obtain a boundary pointwise gradient estimate on a parabolic half cube        Q          2      R        ∩  {  (      x          1        ,      x    ′    ,  t  )  ∈            R              n      +      1        :      x          1        >  0  } for nonlinear parabolic equations with measurable nonlinearities, which are only assumed to be measurable in        x          1      -variable. The estimates are obtained in terms of Riesz potential of the right-hand side measure and the oscillation of the boundary data, where the boundary data is given on        Q          2      R        ∩  {  (      x          1        ,      x    ′    ,  t  )  ∈            R              n      +      1        :      x          1        =  0  }.}
}