## Regularity of the derivatives of solutions to certain degenerate elliptic equations.(English)Zbl 0554.35048

The author considers the degenerate elliptic equation $$div(| \nabla u|^{p-2}\nabla u)=0$$ on some domain $$\Omega \subset {\mathbb{R}}^ n$$ with $$p\in (1,\infty)$$ and poves that $$u\in W^ p_ 1$$ belongs in fact to $$C^{1,\alpha}_{loc}$$ with some $$\alpha =\alpha (p,n)$$, thereby extending results of N. Ural’tseva [Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 7, 184-221 (1968; Zbl 0196.125)] and L. C. Evans [J. Differ. Equations 45, 356-373 (1982; Zbl 0508.35036), different proof] to the case $$1<p<2$$. Similar results for systems of this type were achieved by P. Tolksdorf [Ann. Mat. Pura Appl., IV. Ser. 134, 241-266 (1983; Zbl 0538.35034)].
Reviewer: M.Wiegner

### MSC:

 35J70 Degenerate elliptic equations 35D10 Regularity of generalized solutions of PDE (MSC2000) 35B65 Smoothness and regularity of solutions to PDEs

regularity

### Citations:

Zbl 0196.125; Zbl 0508.35036; Zbl 0538.35034
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