Volume 4, Issue 3
The Boundedness for Generalized Solutions of Quasilinear Elliptic Equations

Liang Xiting

DOI:

J. Part. Diff. Eq.,4(1991),pp.79-88

Published online: 1991-04

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  • Abstract

Under the appropriate conditions on u, the generalized solution of the elliptic equation ∫_G {∇v ⋅ A(x, u, ∇u) + vB(x, u, ∇u)}dx = 0, \quad ∀v ∈ {\WW}¹_p(G) ∩ L_∞(G) for which even the natural growth condition p(1 - 1/p^∗) < ϒ < p is permitted, the local and global boundedness of u are proved.

  • Keywords

Elliptic equation critical exponent natural growth condition generalized solution boundedness H&#246lder continuity

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COPYRIGHT: © Global Science Press

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@Article{JPDE-4-79, author = {Liang Xiting}, title = {The Boundedness for Generalized Solutions of Quasilinear Elliptic Equations}, journal = {Journal of Partial Differential Equations}, year = {1991}, volume = {4}, number = {3}, pages = {79--88}, abstract = { Under the appropriate conditions on u, the generalized solution of the elliptic equation ∫_G {∇v ⋅ A(x, u, ∇u) + vB(x, u, ∇u)}dx = 0, \quad ∀v ∈ {\WW}¹_p(G) ∩ L_∞(G) for which even the natural growth condition p(1 - 1/p^∗) < ϒ < p is permitted, the local and global boundedness of u are proved.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5777.html} }
TY - JOUR T1 - The Boundedness for Generalized Solutions of Quasilinear Elliptic Equations AU - Liang Xiting JO - Journal of Partial Differential Equations VL - 3 SP - 79 EP - 88 PY - 1991 DA - 1991/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5777.html KW - Elliptic equation KW - critical exponent KW - natural growth condition KW - generalized solution KW - boundedness KW - Hölder continuity AB - Under the appropriate conditions on u, the generalized solution of the elliptic equation ∫_G {∇v ⋅ A(x, u, ∇u) + vB(x, u, ∇u)}dx = 0, \quad ∀v ∈ {\WW}¹_p(G) ∩ L_∞(G) for which even the natural growth condition p(1 - 1/p^∗) < ϒ < p is permitted, the local and global boundedness of u are proved.
Liang Xiting. (1970). The Boundedness for Generalized Solutions of Quasilinear Elliptic Equations. Journal of Partial Differential Equations. 4 (3). 79-88. doi:
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