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REGULARITY OF H1 ∩Ln((γ-1)/(2-γ)) WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS
He Xudong, Chen Baoyao
Acta mathematica scientia,Series B. 1990, 10 (2):
173-184.
Let us consider the following elliptic systems of second order -Dα(Aiα(x, u, Du))=Bi(x, u, Du), i=1, …, N, x∈Ω⊂Rn, n ≥ 3 (1) and suppose ⅰ)|Aiα(x, u, Du)| ≤ L(1+|Du|); ⅱ) (1+|p|)-1 Aiα(x, u, p)are Hölder-continuous functions with some exponent δ on Ω×RN uniformly with respect to p, i.e.
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