Results 1  10
of
15
CLASSIFICATION OF BLOWUP LIMITS FOR SU(3) SINGULAR TODA SYSTEMS
"... ABSTRACT. We prove that for singular SU(3) Toda systems, the weak limits of the energy belong to a finite set. For more general systems we prove a uniform estimate for fully blownup solutions. Our method uses a selection process and a careful study of the interaction of bubbling solutions. 1. ..."
Abstract

Cited by 10 (5 self)
 Add to MetaCart
(Show Context)
ABSTRACT. We prove that for singular SU(3) Toda systems, the weak limits of the energy belong to a finite set. For more general systems we prove a uniform estimate for fully blownup solutions. Our method uses a selection process and a careful study of the interaction of bubbling solutions. 1.
Malchiodi A.: An improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations
 Commun. Math. Phys
, 2013
"... ar ..."
An existence result for the meanfield equation on compact surfaces in a doubly supercritical regime
 Proc. Royal Soc. Edinburgh A 143 (2013
"... ar ..."
(Show Context)
A note on compactness properties of the singular Toda system
"... In this note, we consider blowup for solutions of the SU(3) Toda system on a compact surface Σ. In particular, we give a complete proof of the compactness result stated by Jost, Lin and Wang in [11] and we extend it to the case of singularities. This is a necessary tool to find solutions through va ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
In this note, we consider blowup for solutions of the SU(3) Toda system on a compact surface Σ. In particular, we give a complete proof of the compactness result stated by Jost, Lin and Wang in [11] and we extend it to the case of singularities. This is a necessary tool to find solutions through variational methods.
LOCAL PROFILE OF FULLY BUBBLING SOLUTIONS TO SU(N+1) TODA SYSTEMS
"... ABSTRACT. In this article we prove that for locally defined singular SU(n + 1) Toda systems in R 2, the profile of fully bubbling solutions near the singular source can be accurately approximated by global solutions. The main ingredients of our new approach are the classification theorem of LinWei ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
ABSTRACT. In this article we prove that for locally defined singular SU(n + 1) Toda systems in R 2, the profile of fully bubbling solutions near the singular source can be accurately approximated by global solutions. The main ingredients of our new approach are the classification theorem of LinWeiYe [20] and the nondegeneracy of the linearized Toda system [20], which make us overcome the difficulties that come from the lack of symmetry and the singular source. 1.
On Nontopological Solutions of the A2 and
, 2013
"... For any rank 2 of simple Lie algebra, the relativistic ChernSimons system has the following form: ∆u1 + ( ∑2 i=1K1ie ui −∑2i=1∑2j=1 euiK1ieujKij) = 4pi N1∑ j=1 δpj ∆u2 + ( ∑2 i=1K2ie ui −∑2i=1∑2j=1 euiK2ieujKij) = 4pi N2∑ j=1 δqj in R2, (0.1) where K is the Cartan matrix of rank 2. There are thre ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
For any rank 2 of simple Lie algebra, the relativistic ChernSimons system has the following form: ∆u1 + ( ∑2 i=1K1ie ui −∑2i=1∑2j=1 euiK1ieujKij) = 4pi N1∑ j=1 δpj ∆u2 + ( ∑2 i=1K2ie ui −∑2i=1∑2j=1 euiK2ieujKij) = 4pi N2∑ j=1 δqj in R2, (0.1) where K is the Cartan matrix of rank 2. There are three Cartan matrix of rank 2: A2, B2 and G2. A longstanding open problem for (0.1) is the question of the existence of nontopological solutions. In this paper, we consider the A2 and B2 case. We prove the existence of nontopological solutions under the condition that either ∑N1 j=1 pj =∑N2 j=1 qj or ∑N1 j=1 pj 6=
j=1
, 2012
"... For any rank 2 of simple Lie algebra, the relativistic ChernSimons system has the following form: ..."
Abstract
 Add to MetaCart
(Show Context)
For any rank 2 of simple Lie algebra, the relativistic ChernSimons system has the following form: