Classification of radial solutions to equations related to Caffarelli–Kohn–Nirenberg inequalities

Authors

John Villavert, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

2-2020

Abstract

This article studies the qualitative and quantitative properties of radial solutions to an elliptic equation related to the Euler–Lagrange equations for certain sharp Caffarelli–Kohn–Nirenberg inequalities. Namely, we examine the equation

−div(|x|aDu)=|x|bup, u>0, in RN, where p>1, N≥2, N−2+a≥0 and b>−N. The main results establish the properties of radially symmetric solutions including existence, uniqueness, and classification results as well as results on the asymptotic and intersecting behaviour of such solutions.

Comments

Original published version available at https://doi.org/10.1007/s10231-019-00879-0

Recommended Citation

Villavert, J. Classification of radial solutions to equations related to Caffarelli–Kohn–Nirenberg inequalities. Annali di Matematica 199, 299–315 (2020). https://doi.org/10.1007/s10231-019-00879-0

Publication Title

Annali di Matematica

DOI

10.1007/s10231-019-00879-0