In this paper we are concerned with a family of elliptic operators L-epsilon represented as sum of square vector fields, whose limit is an Hormander type operator L. It is well known that each operator L_epsilon admits a fundamental solution. Here we establish a priori estimates uniform in epsilon of the fundamental solution, using a generalization of the freezing and lifting technique of Rothschild and Stein. As a consequence we deduce some a priori estimates uniform in epsilon, for solutions of the approximated equation. These estimates can be used in particular while studying regularity of viscosity solutions of nonlinear equations represented in terms of vector fields.

Uniform Estimates of the fundamental solution for a family of hypoelliptic operators / G. Citti; M. Manfredini. - In: POTENTIAL ANALYSIS. - ISSN 0926-2601. - STAMPA. - 25:(2006), pp. 147-164. [10.1007/s11118-006-9014-4]

Uniform Estimates of the fundamental solution for a family of hypoelliptic operators

CITTI, GIOVANNA;MANFREDINI, MARIA
2006

Abstract

In this paper we are concerned with a family of elliptic operators L-epsilon represented as sum of square vector fields, whose limit is an Hormander type operator L. It is well known that each operator L_epsilon admits a fundamental solution. Here we establish a priori estimates uniform in epsilon of the fundamental solution, using a generalization of the freezing and lifting technique of Rothschild and Stein. As a consequence we deduce some a priori estimates uniform in epsilon, for solutions of the approximated equation. These estimates can be used in particular while studying regularity of viscosity solutions of nonlinear equations represented in terms of vector fields.
2006
Uniform Estimates of the fundamental solution for a family of hypoelliptic operators / G. Citti; M. Manfredini. - In: POTENTIAL ANALYSIS. - ISSN 0926-2601. - STAMPA. - 25:(2006), pp. 147-164. [10.1007/s11118-006-9014-4]
G. Citti; M. Manfredini
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/8727
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 14
social impact