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 10 (Ω). In addition, by requiring C lmij =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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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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Lair, A.V. Quasilinear elliptic systems. Annali di Matematica 116, 17–56 (1978). https://doi.org/10.1007/BF02413866
- Weak Solution
- Bounded Domain
- Auxiliary Function
- Elliptic System
- Author Study