A semi-linear problem for the Heisenberg laplacian

Isabeau Birindelli; Alessandra Cutrì

Displaying similar documents to “A semi-linear problem for the Heisenberg laplacian”

One dimensional symmetry in the Heisenberg group

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Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Liouville theorems for semilinear equations on the Heisenberg group

I. Birindelli, I. Capuzzo Dolcetta, A. Cutrì (1997)

Annales de l'I.H.P. Analyse non linéaire

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Generalized maximum principle and evaluation of the first eigenvalue for Heisenberg-type operators with discontinuous coefficients

M. Chicco, M. R. Lancia (2001)

Bollettino dell'Unione Matematica Italiana

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Precedenti risultati riguardanti il principio di massimo generalizzato e la valutazione del primo autovalore per operatori uniformemente ellittici di tipo variazionale vengono estesi agli operatori subellittici di tipo Heisenberg non simmetrici e a coefficienti discontinui.

Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation

Nicola Garofalo, Ermanno Lanconelli (1990)

Annales de l'institut Fourier

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A recent result of Bahouri shows that continuation from an open set fails in general for solutions of $ℒ u = V u$ where $V \in C^{\infty}$ and $ℒ = \sum_{j = 1}^{N - 1} X_{j}^{2}$ is a (nonelliptic) operator in $R^{N}$ satisfying Hörmander’s condition for hypoellipticity. In this paper we study the model case when $ℒ$ is the subelliptic Laplacian on the Heisenberg group and $V$ is a zero order term which is allowed to be unbounded. We provide a sufficient condition, involving a first order differential inequality, for nontrivial solutions of $ℒ u = V u$ to have a...

On the Liouville property for sublaplacians

Italo Capuzzo Dolcetta, Alessandra Cutrì (1997)

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Extension of Díaz-Saá's inequality in R and application to a system of p-Laplacian.

Karim Chaïb (2002)

Publicacions Matemàtiques

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The purpose of this paper is to extend the Díaz-Saá’s inequality for the unbounded domains as R^N. The proof is based on the Picone’s identity which is very useful in problems involving p-Laplacian. In a second part, we study some properties of the first eigenvalue for a system of p-Laplacian. We use Díaz-Saá’s inequality to prove uniqueness and Egorov’s theorem for the isolation. These results generalize J. Fleckinger, R. F. Manásevich, N. M. Stavrakakis...