Decay estimates for solutions to non-autonomous critical p-Laplace problems

2025/02/27 by Laura Baldelli, Baldelli, Laura, Umberto Guarnotta +1 · 1 citation
Engineering · Mathematics · #35B08 #35B45 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2502.19819

openalex publication_date 2025/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove optimal decay estimates for positive solutions to elliptic p-Laplacian problems in the entire Euclidean space, when a critical nonlinearity with a decaying source term is considered. Also gradient decay estimates are furnished. Our results extend previous theorems in the literature, in which a purely critical reaction is treated. The technique is based on a priori estimates, regularity results, and rescaling arguments, combined with the doubling lemma.

Cited by

• Existence and decay for a Grushin problem in ℝ^N with singular, convective, critical reaction

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