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Complex Variables and Elliptic Equations
An International Journal
Volume 57, 2012 - Issue 2-4: Complex and Real Analysis and Applications, in honour of Professor Robert P. Gilbert on the occasion of his 80th birthday
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Original Articles

Heat kernels for a class of degenerate elliptic operators using stochastic method

Ovidiu Calin Department of Mathematics, Eastern Michigan University, Ypsilanti, Michigan, 48197, USA
,
Der-Chen Chang Department of Mathematics and Department of Computer Science, Georgetown University, Washington, D.C. 20057, USACorrespondence[email protected]
,
Jishan Hu Department of Mathematics, Hong Kong University of Science and Technology, Kowloon, Hong Kong
&
Yutian LI Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
Pages 155-168 | Received 02 Mar 2011, Accepted 13 Apr 2011, Published online: 20 Sep 2011

References

  • Baouendi , MS and Goulaouic , C . 1972 . Non-analytic hypoellipticity for some degenerate elliptic operators . Bull. Amer. Math. Soc. , 78 : 483 – 486 .
  • Calin , O , Chang , DC , Furutani , K and Iwasaki , C . 2010 . “ Heat Kernels for Elliptic and Sub-elliptic Operators–Methods and Techniques ” . In Applied and Numerical Harmonic Analysis , Boston–Basel–Berlin : Birkhaüser .
  • Beals , R , Gaveau , B , Greiner , P and Kannai , Y . 1999 . Exact fundamental solutions for a class of degenerate elliptic operators . Commun. Partial Diff. Eq. , 24 ( 2, 3 ) : 719 – 742 .
  • Calin , O , Chang , DC , Hu , J and Li , Y . 2011 . On heat kernels of a class of degenerate elliptic operators . J. Nonlinear Convex Anal. , 12 : 309 – 340 .
  • Calin , O and Chang , DC . 2011 . Heat kernels for differential operators with radical function coefficients . Taiwanese J. Math. , 15 : 1629 – 1636 .
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  • Gaveau , B . 1978 . Systémes Dynamiques associés a certains opérateurs hypoelliptiques . Bull. Sci. Math. , 102 : 203 – 229 .
  • Øksendal , B . 2003 . Stochastic Differential Equations, An Introduction with Applications , 6th , Berlin : Springer .
  • Beals , R , Gaveau , B and Greiner , P . 1999 . Green's functions for some highly degenerate elliptic operators . J. Funct. Anal. , 165 : 407 – 429 .
  • Grushin , VV . 1970 . On a class of hypoelliptic operators . Math. USSR Sb. , 125 : 458 – 476 .

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