Greco, Luigi; Verde, Anna A regularity property of \(p\)-harmonic functions. (English) Zbl 0952.35039 Ann. Acad. Sci. Fenn., Math. 25, No. 2, 317-323 (2000). The paper considers the equation \[ \text{div}((G(x)Du,Du)^{(p-2)/2}G(x)Du)=0, \] where \(G\) is a positive definite symmetric matrix from \(L^\infty \cup VMO\). For every \(r>1\) and for \(p\) close to 2, every very weak solution of class \(W^{1,r}_{\text{loc}}\) is proved to be of class \(W^{1,q}_{\text{loc}}\) for all \(q<\infty\). Reviewer: Evgeniy A.Kalita (Donetsk) Cited in 4 Documents MSC: 35J60 Nonlinear elliptic equations 35B65 Smoothness and regularity of solutions to PDEs Keywords:\(p\)-harmonic functions; regularity; very weak solutions; Hodge decomposition PDFBibTeX XMLCite \textit{L. Greco} and \textit{A. Verde}, Ann. Acad. Sci. Fenn., Math. 25, No. 2, 317--323 (2000; Zbl 0952.35039) Full Text: EuDML EMIS