arXiv subjects

Gabriele Giannone

Publications and source records attributed to Gabriele Giannone.

2 recordsLinked to original sources

arXiv2025

Local boundedness of weak solutions to elliptic equations under unbalanced Orlicz growth conditions

We establish sufficient conditions for the local boundedness of weak solutions to a broad class of nonlinear elliptic equations in divergence form, under unbalanced growth conditions on the stress field. Our analysis is carried out in a non-variational setting, with no symmetry or structural assumptions on the operator. The ellipticity and growth are prescribed via distinct Young functions, leading to a Orlicz-type setting that captures a wide class of nonstandard behaviors. As a special case, the theory encompasses and extends the known results on equations with $p,q$-growth.

math.AP↗

arXiv2025

Regularizing effects for an elliptic system of singular equations

A system of two singular semi-linear elliptic equations, patterned after the Schr\"odinger-Maxwell system, is considered. If the reaction term of the first equation contains a datum $f\in L^m$, 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.

math.AP↗