## Summary

The quasilinear elliptic system

*1*⩽i⩽N, x in a bounded domain Ω, and U=*0* on the boundary of Ω is studied. Under various assumptions regarding the auxiliary functions C, B, and F, the author studies weak existence, uniqueness, and stability in H
^{1}_{0}
(Ω). In addition, by requiring C
^{lm}_{ij}
=*0* for i ≠ j, it is proved that such weak solutions have bounded L_{∞}(Ω) norm and satisfy a Hölder condition on the closure of Ω.

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## Author information

### Affiliations

## Additional information

Entrata in Redazione il 23 giugno 1976.

These results are contained in the author's doctoral dissertation written under the direction of Prof.W. T. Ford at Texas Tech. University.

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### Cite this article

Lair, A.V. Quasilinear elliptic systems.
*Annali di Matematica* **116, **17–56 (1978). https://doi.org/10.1007/BF02413866

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### Keywords

- Weak Solution
- Bounded Domain
- Auxiliary Function
- Elliptic System
- Author Study