BMO estimates for the \(p\)-Laplacian
The authors prove BMO estimates of the inhomogeneous \(p\)-Laplace system \[ -\text{div }(|\nabla u|^{p-2}\nabla u)=\text{div }f,\qquad p\in(1,\infty). \] It is shown that \(f\in\) BMO implies \(|\nabla u|^{p-2}\nabla u\in\) BMO, which is the limiting case of the nonlinear Calderón-Zygmund theory. Moreover, it is proved that \(A(\nabla u)=\varphi'(|\nabla u|)\frac{\nabla u}{|\nabla u|}\) inherits the Campanato and VMO regularity of \(f.\)
scientific article; zbMATH DE number 5987796
scientific article