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Volume 24, Issue 1
Regularity Theorems for Elliptic and Hypoelliptic Operators Via the Global Relation

A. C. L. Ashton

DOI: 10.4208/jpde.v24.n1.6

J. Part. Diff. Eq., 24 (2011), pp. 83-96.

Published online: 2011-02

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  • Abstract

In this paperwe give a newproof regarding the regularity of solutions to hypoelliptic partial differential equations with constant coefficients. On the assumption of existence, we provide a spectral representation for the solution and use this spectral representation to deduce regularity results. By exploiting analyticity properties of the terms within the spectral representation, we are able to give simple estimates for the size of the derivatives of the solutions and interpret them in terms of Gevrey classes.

  • Keywords

Hypoelliptic operators constant coefficient distributions

  • AMS Subject Headings

46Fxx 32Axx 35H10 35C15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-24-83, author = {A. C. L. Ashton }, title = {Regularity Theorems for Elliptic and Hypoelliptic Operators Via the Global Relation}, journal = {Journal of Partial Differential Equations}, year = {2011}, volume = {24}, number = {1}, pages = {83--96}, abstract = {

In this paperwe give a newproof regarding the regularity of solutions to hypoelliptic partial differential equations with constant coefficients. On the assumption of existence, we provide a spectral representation for the solution and use this spectral representation to deduce regularity results. By exploiting analyticity properties of the terms within the spectral representation, we are able to give simple estimates for the size of the derivatives of the solutions and interpret them in terms of Gevrey classes.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v24.n1.6}, url = {http://global-sci.org/intro/article_detail/jpde/5199.html} }
TY - JOUR T1 - Regularity Theorems for Elliptic and Hypoelliptic Operators Via the Global Relation AU - A. C. L. Ashton JO - Journal of Partial Differential Equations VL - 1 SP - 83 EP - 96 PY - 2011 DA - 2011/02 SN - 24 DO - http://doi.org/10.4208/jpde.v24.n1.6 UR - https://global-sci.org/intro/article_detail/jpde/5199.html KW - Hypoelliptic operators KW - constant coefficient KW - distributions AB -

In this paperwe give a newproof regarding the regularity of solutions to hypoelliptic partial differential equations with constant coefficients. On the assumption of existence, we provide a spectral representation for the solution and use this spectral representation to deduce regularity results. By exploiting analyticity properties of the terms within the spectral representation, we are able to give simple estimates for the size of the derivatives of the solutions and interpret them in terms of Gevrey classes.

A. C. L. Ashton . (2011). Regularity Theorems for Elliptic and Hypoelliptic Operators Via the Global Relation. Journal of Partial Differential Equations. 24 (1). 83-96. doi:10.4208/jpde.v24.n1.6
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