In this paper we prove Poincar ́e and Sobolev inequalities for differ-ential forms in the Rumin’s contact complex on Heisenberg groups. Inparticular, we deal with endpoint values of the exponents, obtaining fi-nally estimates akin to exponential Trudinger inequalities for scalar func-tion. These results complete previous results obtained by the authors awayfrom the exponential case. From the geometric point of view, Poincar ́eand Sobolev inequalities for differential forms provide a quantitative for-mulation of the vanishing of the cohomology. They have also applicationsto regularity issues for partial differential equations.

ORLICZ SPACES AND ENDPOINT SOBOLEV-POINCAR ́EINEQUALITIES FOR DIFFERENTIAL FORMS INHEISENBERG GROUPS / A. Baldi, B. Franchi, P. Pansu. - In: LE MATEMATICHE. - ISSN 0373-3505. - STAMPA. - 75:1(2020), pp. 167-194. [10.4418/2020.75.1.9]

ORLICZ SPACES AND ENDPOINT SOBOLEV-POINCAR ́EINEQUALITIES FOR DIFFERENTIAL FORMS INHEISENBERG GROUPS

A. Baldi;B. Franchi
;
2020

Abstract

In this paper we prove Poincar ́e and Sobolev inequalities for differ-ential forms in the Rumin’s contact complex on Heisenberg groups. Inparticular, we deal with endpoint values of the exponents, obtaining fi-nally estimates akin to exponential Trudinger inequalities for scalar func-tion. These results complete previous results obtained by the authors awayfrom the exponential case. From the geometric point of view, Poincar ́eand Sobolev inequalities for differential forms provide a quantitative for-mulation of the vanishing of the cohomology. They have also applicationsto regularity issues for partial differential equations.
2020
ORLICZ SPACES AND ENDPOINT SOBOLEV-POINCAR ́EINEQUALITIES FOR DIFFERENTIAL FORMS INHEISENBERG GROUPS / A. Baldi, B. Franchi, P. Pansu. - In: LE MATEMATICHE. - ISSN 0373-3505. - STAMPA. - 75:1(2020), pp. 167-194. [10.4418/2020.75.1.9]
A. Baldi, B. Franchi, P. Pansu
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/728920
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