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Volume 21, Issue 4
Global Lp Estimates for the Parabolic Equation of the Bi-harmonic Type

Fengping Yao & Shulin Zhou

J. Part. Diff. Eq., 21 (2008), pp. 315-334.

Published online: 2008-11

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  • Abstract
In this paper similarly to the second-order case, we give an elementary and straightforward proof of global L^p estimates for the initial-value parabolic problem of the bi-harmonic type. Moreover, we obtain the existence and uniqueness of the solutions in the suitable space using the potential theory, Marcinkiewicz interpolation theorem and approximation argument. Meanwhile, by the same approach we can deal with the general polyharmonic cases.
  • Keywords

Bi-harmonic parabolic L^p estimates existence uniqueness

  • AMS Subject Headings

35A05 35K25 35G05.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-21-315, author = {Fengping Yao and Shulin Zhou }, title = {Global Lp Estimates for the Parabolic Equation of the Bi-harmonic Type}, journal = {Journal of Partial Differential Equations}, year = {2008}, volume = {21}, number = {4}, pages = {315--334}, abstract = { In this paper similarly to the second-order case, we give an elementary and straightforward proof of global L^p estimates for the initial-value parabolic problem of the bi-harmonic type. Moreover, we obtain the existence and uniqueness of the solutions in the suitable space using the potential theory, Marcinkiewicz interpolation theorem and approximation argument. Meanwhile, by the same approach we can deal with the general polyharmonic cases.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5285.html} }
TY - JOUR T1 - Global Lp Estimates for the Parabolic Equation of the Bi-harmonic Type AU - Fengping Yao & Shulin Zhou JO - Journal of Partial Differential Equations VL - 4 SP - 315 EP - 334 PY - 2008 DA - 2008/11 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5285.html KW - Bi-harmonic KW - parabolic KW - L^p estimates KW - existence KW - uniqueness AB - In this paper similarly to the second-order case, we give an elementary and straightforward proof of global L^p estimates for the initial-value parabolic problem of the bi-harmonic type. Moreover, we obtain the existence and uniqueness of the solutions in the suitable space using the potential theory, Marcinkiewicz interpolation theorem and approximation argument. Meanwhile, by the same approach we can deal with the general polyharmonic cases.
Fengping Yao and Shulin Zhou . (2008). Global Lp Estimates for the Parabolic Equation of the Bi-harmonic Type. Journal of Partial Differential Equations. 21 (4). 315-334. doi:
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