Quasilinear elliptic systems

Summary

The quasilinear elliptic system

$$\sum\limits_{l{\text{ = 1}}}^n {\frac{\partial }{{\partial x_l }}\left\{ {\sum\limits_{j = 1}^N {\sum\limits_{m = 1}^n {C_{ij}^{lm} [x,U]\frac{{\partial U^j }}{{\partial x_m }} + B_i^l [x,U]} } } \right\} + F_i [x,U] = 0} $$

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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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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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