×

A regularity property of \(p\)-harmonic functions. (English) Zbl 0952.35039

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 \(q<\infty\).

MSC:

35J60 Nonlinear elliptic equations
35B65 Smoothness and regularity of solutions to PDEs
PDFBibTeX XMLCite
Full Text: EuDML EMIS