On some Extrapolation in Generalized Grand Morrey Spaces with Applications to PDEs

Rubio de Francia’s extrapolation in generalized grand Morrey spaces is derived. This result is applied to the investigation of the regularity of solutions for the second order partial differential equations with discontinuous coefficients in the framework of generalized grand Morrey spaces under the Muckenhoupt condition on weights. Density properties for these spaces are also investigated.