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Volume 17, Issue 4
Maximum Principles for Second-order Parabolic Equations

Antonio Vitolo

J. Part. Diff. Eq., 17 (2004), pp. 289-302.

Published online: 2004-11

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  • Abstract

This paper is the parabolic counterpart of previous ones about elliptic operators in unbounded domains. Maximum principles for second-order linear parabolic equations are established showing a variant of the ABP-Krylov-Tso estimate, based on the extension of a technique introduced by Cabré, which in turn makes use of a lower bound for super-solutions due to Krylov and Safonov. The results imply the uniqueness for the Cauchy-Dirichlet problem in a large class of in nite cylindrical and non-cylindrical domains.

  • Keywords

Maximum principle ABP estimate parabolic equations

  • AMS Subject Headings

35K10 35K15 35K20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-17-289, author = {Antonio Vitolo }, title = {Maximum Principles for Second-order Parabolic Equations}, journal = {Journal of Partial Differential Equations}, year = {2004}, volume = {17}, number = {4}, pages = {289--302}, abstract = {

This paper is the parabolic counterpart of previous ones about elliptic operators in unbounded domains. Maximum principles for second-order linear parabolic equations are established showing a variant of the ABP-Krylov-Tso estimate, based on the extension of a technique introduced by Cabré, which in turn makes use of a lower bound for super-solutions due to Krylov and Safonov. The results imply the uniqueness for the Cauchy-Dirichlet problem in a large class of in nite cylindrical and non-cylindrical domains.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5394.html} }
TY - JOUR T1 - Maximum Principles for Second-order Parabolic Equations AU - Antonio Vitolo JO - Journal of Partial Differential Equations VL - 4 SP - 289 EP - 302 PY - 2004 DA - 2004/11 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5394.html KW - Maximum principle KW - ABP estimate KW - parabolic equations AB -

This paper is the parabolic counterpart of previous ones about elliptic operators in unbounded domains. Maximum principles for second-order linear parabolic equations are established showing a variant of the ABP-Krylov-Tso estimate, based on the extension of a technique introduced by Cabré, which in turn makes use of a lower bound for super-solutions due to Krylov and Safonov. The results imply the uniqueness for the Cauchy-Dirichlet problem in a large class of in nite cylindrical and non-cylindrical domains.

Antonio Vitolo . (2004). Maximum Principles for Second-order Parabolic Equations. Journal of Partial Differential Equations. 17 (4). 289-302. doi:
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