Electron. J. Differential Equations, Vol. 2017 (2017), No. 92, pp. 1-17.

Properties of scales of Kato classes, Bessel potentials, Morrey spaces, and a weak Harnack inequality for non-negative solutions of elliptic equations

Rene Erlin Castillo, Julio C. Ramos-Fernandez, Edixon M. Rojas

Abstract:
In this article, we study some basic properties of the scale of Kato classes related with the Bessel kernel, Lorentz spaces, and Morrey spaces. Also we characterize the weak Harnack inequality for non-negative solutions of elliptic equations in terms of the Bessel kernel and the Kato classes of order $\alpha$.

Submitted December 21, 2016. Published March 30, 2017.
Math Subject Classifications: 35B05, 35J10, 35J15.
Key Words: Kato class; Bessel potential; Riesz potential; Lorentz space; weak Harnack inequality.

Show me the PDF file (263 KB), TEX file for this article.

René Erlín Castillo
Departamento de Matemáticas
Universidad Nacional de Colombia
Bogotá, Colombia
email: recastillo@unal.edu.co
Julio C. Ramos-Fernández
Departamento de Matemáticas
Universidad de Oriente
6101 Cumaán Edo.
Sucre, Venezuela
email: jcramos@udo.edu.ve
Edixon M. Rojas
Departamento de Matemáticas
Universidad Nacional de Colombia
Bogotá, Colombia
email: emrojass@unal.edu.co

Return to the EJDE web page