TY - JOUR
T1 - Regularity Results for Nonlinear Systems of Partial Differential Equations Under Weak Ellipticity Conditions
JO - Journal of Partial Differential Equations
VL - 3
SP - 217
EP - 225
PY - 2000
DA - 2000/08
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5508.html
KW - Regularity
KW - nonlinear system
KW - ellipticity
KW - weak solution
KW - Lipschitz continuity
AB -  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.