Biharmonic nonlinear scalar field equations

Jarosław Mederski, Jakub Siemianowski

We prove a Brezis-Kato-type regularity result for weak solutions to the biharmonic nonlinear equation $${\Delta }^{2}u=g(x,u)\text{in }{\mathbb{R}}^N$$ with a Carathéodory function $…