Regularizing effect of absorption terms in singular and degenerate elliptic problems

Abstract

In this paper we study the existence and regularity of solutions to the following singular problemproving that the lower order term u|u| s−1 has some regularizing effects on the solutions in the case of an elliptic operator with degenerate coercivity.

Existence and regularity of positive solutions for Schrödinger-Maxwell system with singularity

“…We refer the readers to Refs. [8,11,16,17]. In the case θ = 0 many works have appeared concerning the existence and regularity of elliptic systems.…”

Nonlinear Elliptic Equations With Variable Exponents Involving Singular Nonlinearity

“…For costant-exponent cases (i.e., p(x) = p, r(x) = r and γ(x) = γ), the existence and regularity of solutions to problem (1.1) are studied in [2,14,28,29]. They proved that the solution was in W 1,q 0 (Ω) and u r+γ belongs to L 1 (Ω), where q = pr p+1−γ .…”