Quasilinear elliptic systems
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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.
KeywordsWeak Solution Bounded Domain Auxiliary Function Elliptic System Author Study
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