Nonlinear anisotropic parabolic equations in with locally integrable data

Abstract

In this paper, we prove existence and regularity of weak solutions for a class of nonlinear anisotropic parabolic problems in RN with locally integrable data. Our approach is based on the anisotropic Sobolev inequality, a smoothness, and compactness results. Copyright © 2012 John Wiley & Sons, Ltd.

Nonlinear anisotropic elliptic equations in with variable exponents and locally integrable data

“…For the constant isotropic case, we refer the reader to [10] and the references therein. The corresponding results for constant case and anisotropic elliptic or parabolic equations are developed in [11][12][13][14]. In this work, we treat the anisotropic elliptic case with locally integrable right-hand side f , in unbounded domain, s i ../ p i ../, and the exponents p i ../, i D 1, : : : , N are restricted as in (5).…”