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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.
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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