Journal of Functional Analysis

2004

DOI: 10.1016/s0022-1236(03)00138-1

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Nonlinear Liouville theorems for some critical problems on H-type groups

Andrea Bonfiglioli

¹

,

Francesco Uguzzoni

²

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Introduction3

Notations and Preliminaries1

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Cited by 54 publications

(35 citation statements)

References 36 publications

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“…[3,11,12,[18][19][20] and the references therein), but at the present time, the greatest part of the literature concerns non-singular problems.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

L p -weak regularity and asymptotic behavior of solutions for critical equations with singular potentials on Carnot groups

¹

2010

Nonlinear Differ. Equ. Appl.

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Abstract. In this paper, we consider a large class of critical problems with singular potentials on Carnot groups. In particular, we prove sharp regularity results in Marcinkiewicz spaces and the exact rate of decay of the solutions. Our general results apply, for instance, to the equation satisfied by the extremals of some relevant Hardy-Sobolev type inequalities on Stratified groups.

“…[3,11,12,[18][19][20] and the references therein), but at the present time, the greatest part of the literature concerns non-singular problems.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

L p -weak regularity and asymptotic behavior of solutions for critical equations with singular potentials on Carnot groups

¹

2010

Nonlinear Differ. Equ. Appl.

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Abstract. In this paper, we consider a large class of critical problems with singular potentials on Carnot groups. In particular, we prove sharp regularity results in Marcinkiewicz spaces and the exact rate of decay of the solutions. Our general results apply, for instance, to the equation satisfied by the extremals of some relevant Hardy-Sobolev type inequalities on Stratified groups.

“…Successively, exploiting this result and by means of a deep analysis developed by Bonfiglioli and Uguzzoni in [5], Loiudice studied in [24] the existence of positive and sign changing solutions for critical problems on Carnot groups, extending to this subelliptic context the results obtained by Brézis and Nirenberg in their pioneering paper [7]. See, among others, the papers [2,8,16,17,30] and references therein for related results.…”

Section: Introductionmentioning

confidence: 90%

Yamabe-Type Equations on Carnot Groups

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²

2016

Potential Anal

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Abstract. This article is concerned with a class of elliptic equations on Carnot groups depending of one real positive parameter and involving a critical nonlinearity. As a special case of our results we prove the existence of at least one nontrivial solution for a subelliptic critical equation defined on a smooth and bounded domain D of the Heisenberg group H n = C n × IR. Our approach is based on pure variational methods and locally sequentially weakly lower semicontinuous arguments.

“…Recall that a H-type group G is a Carnot group of step two in which the group law has the form (see [2])…”

Section: Notations and Preliminariesmentioning

confidence: 99%

A Hardy Inequality on H-Type Groups

2012

Bulletin of the Korean Mathematical Society

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Abstract. We prove a Hardy inequality related to Carnot-Carathéodory distance on H-type groups based on a representation formula on such groups.

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