Hilbert-Haar coordinates and Miranda's theorem in Lie groups

András Domokos; Juan J. Manfredi

doi:10.6092/issn.2240-2829/10582

Autori

András Domokos Department of Mathematics and Statistics, California State University Sacramento, 6000 J Street, Sacramento, CA, 95819 http://orcid.org/0000-0003-2369-4888

Ph. D. University of Pittsburgh 2004.
Professor of Mathematics, California State University at Sacramento.
Juan J. Manfredi Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260 http://orcid.org/0000-0003-3305-8535

Ph. D. 1986, Washington University in Saint Louis.
Foreign member of the Societies Academy (Class of Natural Sciences) of the Royal Norwegian Society of Sciences and Letters (since 2017).
Professor of Mathematics, University of Pittsburgh

DOI:

https://doi.org/10.6092/issn.2240-2829/10582

Parole chiave:

Carnot groups, Engel group, Goursat group, Hilbert-Haar coordinates, subelliptic PDE, weak solutions, interior regularity

Abstract

Studiamo la regolarità interna delle soluzioni di una classe di equazioni quasilineari non degeneri di tipo p-Laplaciano su gruppi di Lie che ammettono un sistema di coordinate di Hilbert-Haar. Si tratta di coordinate rispetto alle quali ogni funzione lineare ha derivate orizzontali simmetrizzate di ordine due nulle. Tutti i gruppi di Carnot di passo due appartengono a questa classe, come anche il gruppo Engel, i gruppi di tipo Goursat e tuti quei gruppi di Carnot di passo tre per i quali i commutatori di ordine tre, diversi da zero, sono linearmente indipendenti.

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