Regularity estimates in weighted Morrey spaces for quasilinear elliptic equations

  • Giuseppe Di Fazio

    Università degli Studi di Catania, Italy
  • Truyen Nguyen

    University of Akron, USA
Regularity estimates in weighted Morrey spaces for quasilinear elliptic equations cover
Download PDF

A subscription is required to access this article.

Abstract

We study regularity for solutions of quasilinear elliptic equations of the form in bounded domains in . The vector field is assumed to be continuous in , and its growth in is like that of the -Laplace operator. We establish interior gradient estimates in weighted Morrey spaces for weak solutions to the equation under a small BMO condition in for . As a consequence, we obtain that is in the classical Morrey space or weighted space whenever is respectively in or , where is any number greater than and is any weight in the Muckenhoupt class . In addition, our two-weight estimate allows the possibility to acquire the regularity for in a weighted Morrey space that is different from the functional space that the data belongs to.

Cite this article

Giuseppe Di Fazio, Truyen Nguyen, Regularity estimates in weighted Morrey spaces for quasilinear elliptic equations. Rev. Mat. Iberoam. 36 (2020), no. 6, pp. 1627–1658

DOI 10.4171/RMI/1178