## Regularity properties of solutions of a class of elliptic-parabolic nonlinear Levi type equations

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- by G. Citti and A. Montanari PDF
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**354**(2002), 2819-2848 Request permission

## Abstract:

In this paper we prove the smoothness of solutions of a class of elliptic-parabolic nonlinear Levi type equations, represented as a sum of squares plus a vector field. By means of a freezing method the study of the operator is reduced to the analysis of a family $L_{\xi _0}$ of left invariant operators on a free nilpotent Lie group. The fundamental solution $\Gamma _{\xi _0}$ of the operator $L_{\xi _0}$ is used as a parametrix of the fundamental solution of the Levi operator, and provides an explicit representation formula for the solution of the given equation. Differentiating this formula and applying a bootstrap method, we prove that the solution is $C^\infty$.## References

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## Additional Information

**G. Citti**- Affiliation: Dipartimento di Matematica, Universita di Bologna, Piazza di Porta S. Donato 5, 40127, Bologna, Italy
- Email: citti@dm.unibo.it
**A. Montanari**- Affiliation: Dipartimento di Matematica, Universita di Bologna, Piazza di Porta S. Donato 5, 40127, Bologna, Italy
- Email: montanar@dm.unibo.it
- Received by editor(s): May 3, 2000
- Received by editor(s) in revised form: August 8, 2001
- Published electronically: February 14, 2002
- Additional Notes: Investigation supported by University of Bologna, founds for selected research topics.
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**354**(2002), 2819-2848 - MSC (2000): Primary 35J70, 35K65; Secondary 22E30
- DOI: https://doi.org/10.1090/S0002-9947-02-02928-8
- MathSciNet review: 1895205