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Volume 13, Issue 3
Regularity Results for Nonlinear Systems of Partial Differential Equations Under Weak Ellipticity Conditions

Yuesheng Zeng

J. Part. Diff. Eq., 13 (2000), pp. 217-225.

Published online: 2000-08

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  • 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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COPYRIGHT: © Global Science Press

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@Article{JPDE-13-217, author = {Yuesheng Zeng }, title = {Regularity Results for Nonlinear Systems of Partial Differential Equations Under Weak Ellipticity Conditions}, journal = {Journal of Partial Differential Equations}, year = {2000}, volume = {13}, number = {3}, pages = {217--225}, 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5508.html} }
TY - JOUR T1 - Regularity Results for Nonlinear Systems of Partial Differential Equations Under Weak Ellipticity Conditions AU - Yuesheng Zeng 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.
Yuesheng Zeng . (2000). Regularity Results for Nonlinear Systems of Partial Differential Equations Under Weak Ellipticity Conditions. Journal of Partial Differential Equations. 13 (3). 217-225. doi:
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