@article{Khan2026, 
author = {Zareen A. Khan and Waqar Afzal and Mujahid Abbas and Daniel Breaz and Luminiţa-Ioana Cotîrlă},
title = {Boundedness of truncated Havin–Maz'ya potentials in Herz spaces with applications to        p    (  ⋅  )-Laplace equations},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {20677-20710},
keywords = {analysis of differential equations, truncated Havin–Maz'ya–Wolff potentials, p(⋅)-Laplace equation, variational methods, variable Herz spaces, boundedness},
url = {https://www.sciopen.com/article/10.3934/math.2026841},
doi = {10.3934/math.2026841},
abstract = {In this paper, we developed a variational framework based on Dirichlet-type energy integrals for the        p    (  ⋅  )-Laplace equation, establishing coercivity and weak lower semicontinuity of the associated functional to guarantee existence and uniqueness of minimizers. The central contribution is a pointwise estimation of weak solutions via fractional truncated potentials, employing Havin–Maz'ya-type nonlinear operators in Herz spaces. Our approach subsumes several earlier results, with classical linear potential estimates recovered as limiting cases.}
}