Regularizing effects for an elliptic system of singular equations

2025/05/25 by Gabriele Giannone, Giannone, Gabriele
#math.AP

paper · pdf · doi:10.48550/arxiv.2505.19177

Abstract

A system of two singular semi-linear elliptic equations, patterned after the Schrödinger-Maxwell system, is considered. If the reaction term of the first equation contains a datum f∈ L^m, existence of positive solutions with finite energy is established for suitable ranges of m. In particular, the results from the theory of elliptic single equations are improved. At the same time, thanks to an approach based on approximation schemes and a priori estimates on the approximated sequences of solutions, it is shown that the integrability assumptions on the datum produce higher integrability of the solutions.

Citations

• Some recent results on singular p-laplacian systems
• Some recent results on singular p-Laplacian equations
• On the Schrödinger-Poisson system with indefinite potential and 3-sublinear nonlinearity
• Regularizing effect of absorption terms in singular problems
• Semilinear elliptic equations with singular nonlinearities
• On a singular nonlinear elliptic boundary-value problem

Related

• Regularizing Effect for a Class of Maxwell-Schrödinger Systems
• A singular Schrödinger-Maxwell system
• Existence and non-existence phenomena for nonlinear elliptic equations with L¹ data and singular reactions
• Note on Regularity theory for Nonlinear elliptic equations
• Regularity up to the boundary for singularly perturbed fully nonlinear elliptic equations