@article{Rouhani2026, 
author = {Behzad Djafari Rouhani and Jan Lang and Osvaldo Méndez},
title = {Limit as    p  (  x  )  →  ∞ of    p  (  x  )-harmonic functions for unbounded    p  (  x  )},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {21799-21818},
keywords = {Luxemburg norm, structural stability, modular vector space, p(x)-Laplacian, variable exponent spaces},
url = {https://www.sciopen.com/article/10.3934/math.2026882},
doi = {10.3934/math.2026882},
abstract = {It is shown that if        p    j   is a sequence of continuous, unbounded exponents on a bounded, Lipschitz domain    Ω  ⊂                    R              n   with    1  <      inf          ∈      Ω            p    j    (  x  ) and        p    j    →  ∞ uniformly, then the sequence    (      u    j    ) of solutions of the        p    j    (  ⋅  )-Laplacian converges to the viscosity solution of a suitable differential operator. The novelty here is that each term of the sequence of exponents    (      p    j    ) is allowed to be unbounded in    Ω.}
}