Asymptotics of Large Solutions of p-Laplace Equations on Cylinders Becoming Unbounded

N. N. Dattatreya

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arXiv · 2505.23600

Asymptotics of Large Solutions of p-Laplace Equations on Cylinders Becoming Unbounded

N. N. Dattatreya

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Abstract

In this article, we study the asymptotic behavior of large solutions for a quasi-linear equation involving the p-Laplacian, defined on a sequence of finite cylindrical domains converging to an infinite cylinder. We demonstrate that the sequence of solutions converges locally, in the Sobolev norm, to a solution of the corresponding cross-sectional problem. Moreover, we establish a convergence rate. As part of our analysis, we extend existing convergence results for the case $p\geq 2$, which previously lacked explicit convergence rates, to the range $1<p<2$. We additionally address solutions with finite Dirichlet boundary data within a unified framework and exhibit that this rate of convergence is independent of the boundary data.

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N. N. Dattatreya. 2025-05-29. Asymptotics of Large Solutions of p-Laplace Equations on Cylinders Becoming Unbounded. https://arxiv.org/abs/2505.23600

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