Decay estimates and symmetry of finite energy solutions to elliptic systems in R^n

TL;DR

This paper investigates finite energy solutions to elliptic systems with power nonlinearities in R^n, establishing decay estimates and symmetry results for positive solutions.

Contribution

It provides sharp decay estimates and symmetry results for finite energy solutions to elliptic systems, advancing understanding of their qualitative behavior.

Findings

Sharp pointwise decay estimates for solutions

Symmetry results for positive solutions

Applicable to systems with power nonlinearities

Abstract

We study a notion of finite energy solutions to elliptic systems with power nonlinearities in R^n. We establish sharp pointwise decay estimates for positive and sign-changing solutions. By using these estimates, we obtain symmetry results when the solutions are positive.