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Annali di Matematica Pura ed Applicata (1923 -)

, Volume 116, Issue 1, pp 17–56 | Cite as

Quasilinear elliptic systems

  • A. V. Lair
Article
  • 55 Downloads

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 0 1 (Ω). In addition, by requiring C ij lm =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.

Keywords

Weak Solution Bounded Domain Auxiliary Function Elliptic System Author Study 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata (1923 -) 1978

Authors and Affiliations

  • A. V. Lair
    • 1
  1. 1.University of South DakotaVermillion

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