Blow-Up Diffusion in Singular Elliptic Problems

Abstract

In this paper, we study a class of nonlinear singular elliptic problems involving a diffusion operator with blow-up behaviour as the solution approaches a finite threshold value. The combination of the singular lower-order term, the blow-up diffusion, and low-regularity data gives rise to significant analytical difficulties. Using the framework of renormalized solutions, we establish the existence of solutions under suitable assumptions on the nonlinear operator and the singular term. We also derive some regularity properties of the obtained solutions. These results contribute to the study of singular elliptic problems with blow-up diffusion and low-regularity data.