Regularity for quasilinear PDEs in Carnot groups via Riemannian approximation

András Domokos; Juan J. Manfredi

doi:10.6092/issn.2240-2829/10589

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.2240-2829/10589

Parole chiave:

Carnot groups, Riemannian approximation, subelliptic, p-Laplacian

Abstract

Sunto. Studiamo la regolarità interna delle soluzioni deboli di EDP, quasilineari subellittiche in gruppi di Carnot, della forma

Σ_i=1^m₁X_i (Φ(|∇_Hu|²)X_iu) = 0.

Qui ∇_Hu = (X₁u,...,X_{m_i}u) è il gradiente orizzontale, δ > 0 e l'esponente p ∈ [2, p^*), dove p^* dipende dal passo ν e dalla dimensione omogenea Q del gruppo ed è dato da

p^* = min {2ν ∕ ν-1 , 2Q+8 ∕ Q-2}.

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