Regularity Results for Nonlinear Systems of Partial Differential Equations Under Weak Ellipticity Conditions

Journal of Partial Differential Equations
Vol. 13 No. 3 (2000), pp. 217-225
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Author(s)
Huaihua Teacher's College, Huaihua 418008, Hunan, China
Abstract
We prove C^{1,α} almost everywhere regularity for weak solutions in the space W^{1,k} (Ω, R^N) of the systems - D_αA^i_α(x,u,Du) = B^i(z,u,Du) under the weak ellipticity condition ∫A(x_0 ,u, p + DΦ) ⋅ DΦdy ≥ λ ∫ (|DΦ|² + |DΦ|^k)dy.
Keywords
Regularity;nonlinear system;ellipticity;weak solution;Lipschitz continuity
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