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Volume 14, Issue 1
Very Weak Solutions of p-Laplacian Type Equations with VMO Coefficients

Shulin Zhou

J. Part. Diff. Eq., 14 (2001), pp. 12-20.

Published online: 2001-02

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  • Abstract
In this note we obtain a new a priori estimate for the very weak solutions of p-Laplacian type equations with VMO coefficients when p is close to 2, and then prove that the very weak solutions of such equations are the usual weak solutions. Our approath is based on the Hodge decomposition and the L^p-estimate for the corresponding linear equations. And this also provides a simpler proof for the results in [1].
  • Keywords

p-Laplacian type VMO coefficients very weak solution

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@Article{JPDE-14-12, author = {}, title = {Very Weak Solutions of p-Laplacian Type Equations with VMO Coefficients}, journal = {Journal of Partial Differential Equations}, year = {2001}, volume = {14}, number = {1}, pages = {12--20}, abstract = { In this note we obtain a new a priori estimate for the very weak solutions of p-Laplacian type equations with VMO coefficients when p is close to 2, and then prove that the very weak solutions of such equations are the usual weak solutions. Our approath is based on the Hodge decomposition and the L^p-estimate for the corresponding linear equations. And this also provides a simpler proof for the results in [1].}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5465.html} }
TY - JOUR T1 - Very Weak Solutions of p-Laplacian Type Equations with VMO Coefficients JO - Journal of Partial Differential Equations VL - 1 SP - 12 EP - 20 PY - 2001 DA - 2001/02 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5465.html KW - p-Laplacian type KW - VMO coefficients KW - very weak solution AB - In this note we obtain a new a priori estimate for the very weak solutions of p-Laplacian type equations with VMO coefficients when p is close to 2, and then prove that the very weak solutions of such equations are the usual weak solutions. Our approath is based on the Hodge decomposition and the L^p-estimate for the corresponding linear equations. And this also provides a simpler proof for the results in [1].
Shulin Zhou . (2019). Very Weak Solutions of p-Laplacian Type Equations with VMO Coefficients. Journal of Partial Differential Equations. 14 (1). 12-20. doi:
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