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

TL;DR

This paper establishes optimal decay rates for positive solutions and their gradients to non-autonomous critical p-Laplace problems in Euclidean space, extending previous results to include decaying source terms.

Contribution

It introduces new decay estimates for solutions with non-autonomous nonlinearities, combining a priori estimates, regularity, and rescaling techniques.

Findings

Optimal decay estimates for solutions and gradients.

Extension of decay results to non-autonomous critical problems.

Use of doubling lemma and rescaling methods.

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.