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On the interior regularity of weak solutions of degenerate elliptic systems (the case \(1<p<2\)). (English) Zbl 0818.35024

The authors study the interior regularity of weak solutions of degenerate elliptic systems of the form \[ - {\partial \over \partial x_ \alpha} a_ i^ \alpha (x,Du) = b_ i (x,u, Du) \] where \(u = (u^ 1, \dots, u^ N)\). Numerous results concerning such systems have been proved in recent years. Here the authors prove some regularity results of the first author [Ann. Mat. Pura Appl. 156, 113-125 (1990; Zbl 0732.35032)] and of S. Campanato [Ann. Mat. Pura Appl. 131, 75-106 (1982; Zbl 0493.35022)] under weaker hypotheses than previously required. In particular, no differentiability assumptions on \(b_ i\) are required.
Reviewer: J.Urbas (Canberra)

MSC:

35J45 Systems of elliptic equations, general (MSC2000)
35D10 Regularity of generalized solutions of PDE (MSC2000)
35J70 Degenerate elliptic equations
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References:

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