A regularity result for singular nonlinear elliptic systems in inverse- power weighted Sobolev spaces (Q795985)

The author studies nonlinear elliptic systems of the form \(div(| x|^{-\gamma}A(x,u)Du)=f, \gamma \in [n-2,n),\) and proves, that a bounded weak solution belonging to the weighted Sobolev space (with weight \(| x|^{-\gamma})\) is in fact Hölder continuous on some small ball containing the origin in the case \(f=0\) and A uniformly elliptic (there is a misprint in the abstract of the paper). A slight generalization was published by the author and \textit{E. W. Stredulinsky} in Commun. Pure Appl. Math. 37, 495-510 (1984). This result has to be compared with the case \(\gamma =0\), where only partial regularity can be expected [cf. \textit{M. Giaguinta,} Multiple integrals in the calculus of variations and nonlinear elliptic systems (Ann. Math. Stud. 105) (1983; Zbl 0516.49003)].