It is shown that if $ p_j $ is a sequence of continuous, unbounded exponents on a bounded, Lipschitz domain $ \Omega\subset {\mathbb R}^n $ with $ 1 < \inf\limits_{\in \Omega}p_j(x) $ and $ p_j\rightarrow \infty $ uniformly, then the sequence $ (u_j) $ of solutions of the $ p_j(\cdot) $-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 $ \Omega $.
Citation: Behzad Djafari Rouhani, Jan Lang, Osvaldo Méndez. Limit as $ p(x)\rightarrow \infty $ of $ p(x) $-harmonic functions for unbounded $ p(x) $[J]. AIMS Mathematics, 2026, 11(7): 21799-21818. doi: 10.3934/math.2026882
It is shown that if $ p_j $ is a sequence of continuous, unbounded exponents on a bounded, Lipschitz domain $ \Omega\subset {\mathbb R}^n $ with $ 1 < \inf\limits_{\in \Omega}p_j(x) $ and $ p_j\rightarrow \infty $ uniformly, then the sequence $ (u_j) $ of solutions of the $ p_j(\cdot) $-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 $ \Omega $.
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Behzad Djafari Rouhani, Jan Lang, Osvaldo Méndez. Limit as $ p(x)\rightarrow \infty $ of $ p(x) $-harmonic functions for unbounded $ p(x) $[J]. AIMS Mathematics, 2026, 11(7): 21799-21818. doi: 10.3934/math.2026882
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