Existence of renormalized solutions to fully anisotropic and inhomogeneous elliptic problems

We will present the proof of existence and uniqueness of renormalized solutions to a broad family of strongly non-linear elliptic equations with lower order terms and data of low integrability. The leading part of the operator satisfies general growth conditions settling the problem in the framework of fully anisotropic and inhomogeneous Musielak-Orlicz spaces. The setting considered in this paper generalized known results in the variable exponents, anisotropic polynomial, double phase and classical Orlicz setting.

Automated summary

This paper presents the proof of existence and uniqueness of renormalized solutions to a broad class of strongly nonlinear elliptic equations, which include lower order terms and data of low integrability. The main operator in the equations satisfies general growth conditions, making the results applicable in the framework of fully anisotropic and inhomogeneous Musielak-Orlicz spaces. The setting considered in this paper extends known results in variable exponents, anisotropic polynomial, double phase, and classical Orlicz settings.