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Volume 8, Issue 2
The Regularity for Solutions of Variational Inequalities

Xiting Liang

J. Part. Diff. Eq., 8 (1995), pp. 145-158.

Published online: 1995-08

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  • Abstract
The regularity for solutions of elliptic equations is rather perfectly solved. But it does not so perfect for that of elliptic variational inequalities. In literature only different special situations are considered. Now the boundedness, C^{0,λ} continuity and C^{1,α} regularity are proved for solutions of one-sided obstacle problems under more general structural conditions, in which the growth orders of u are permitted to reach the critical exponents and the growth order ϒ of the gradient in D is permitted to be super critical as 1 < p < n.
  • Keywords

Elliptic variational inequality one-sided obstacle problem boundedness Holder continuity C^{1 α} regularity

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@Article{JPDE-8-145, author = {Liang , Xiting}, title = {The Regularity for Solutions of Variational Inequalities}, journal = {Journal of Partial Differential Equations}, year = {1995}, volume = {8}, number = {2}, pages = {145--158}, abstract = { The regularity for solutions of elliptic equations is rather perfectly solved. But it does not so perfect for that of elliptic variational inequalities. In literature only different special situations are considered. Now the boundedness, C^{0,λ} continuity and C^{1,α} regularity are proved for solutions of one-sided obstacle problems under more general structural conditions, in which the growth orders of u are permitted to reach the critical exponents and the growth order ϒ of the gradient in D is permitted to be super critical as 1 < p < n.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5648.html} }
TY - JOUR T1 - The Regularity for Solutions of Variational Inequalities AU - Liang , Xiting JO - Journal of Partial Differential Equations VL - 2 SP - 145 EP - 158 PY - 1995 DA - 1995/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5648.html KW - Elliptic variational inequality KW - one-sided obstacle problem KW - boundedness KW - Holder continuity KW - C^{1 KW - α} regularity AB - The regularity for solutions of elliptic equations is rather perfectly solved. But it does not so perfect for that of elliptic variational inequalities. In literature only different special situations are considered. Now the boundedness, C^{0,λ} continuity and C^{1,α} regularity are proved for solutions of one-sided obstacle problems under more general structural conditions, in which the growth orders of u are permitted to reach the critical exponents and the growth order ϒ of the gradient in D is permitted to be super critical as 1 < p < n.
Liang , Xiting. (1995). The Regularity for Solutions of Variational Inequalities. Journal of Partial Differential Equations. 8 (2). 145-158. doi:
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