Nonlinear potential theory for Sobolev spaces on Carnot groups.
Vodop'yanov, S.K., Kudryavtseva, N.A. (2009)
Sibirskij Matematicheskij Zhurnal
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Vodop'yanov, S.K., Kudryavtseva, N.A. (2009)
Sibirskij Matematicheskij Zhurnal
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Jin, Yongyang, Han, Yazhou (2010)
Journal of Inequalities and Applications [electronic only]
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Bruno Franchi, Piotr Hajłasz (2000)
Annales Polonici Mathematici
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We prove that if a Poincaré inequality with two different weights holds on every ball, then a Poincaré inequality with the same weight on both sides holds as well.
Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu (1998)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Lorenzo D’Ambrosio (2005)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We prove some Hardy-type inequalities related to quasilinear second-order degenerate elliptic differential operators . If is a positive weight such that , then the Hardy-type inequalityholds. We find an explicit value of the constant involved, which, in most cases, results optimal. As particular case we derive Hardy inequalities for subelliptic operators on Carnot Groups.
Marco Biroli, Umberto Mosco (1995)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We prove local embeddings of Sobolev and Morrey type for Dirichlet forms on spaces of homogeneous type. Our results apply to some general classes of selfadjoint subelliptic operators as well as to Dirichlet operators on certain self-similar fractals, like the Sierpinski gasket. We also define intrinsic BV spaces and perimeters and prove related isoperimetric inequalities.
Bruno Franchi, Guozhen Lu, Richard L. Wheeden (1995)
Annales de l'institut Fourier
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We derive weighted Poincaré inequalities for vector fields which satisfy the Hörmander condition, including new results in the unweighted case. We also derive a new integral representation formula for a function in terms of the vector fields applied to the function. As a corollary of the versions of Poincaré’s inequality, we obtain relative isoperimetric inequalities.