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Topological methods for an elliptic equations with exponential nonlinearities
"... abstract. We consider a class of variational equations with exponential nonlinearities on compact surfaces. From considerations involving the MoserTrudinger inequality, we characterize some sublevels of the EulerLagrange functional in terms of the topology of the surface and of the data of the equ ..."
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abstract. We consider a class of variational equations with exponential nonlinearities on compact surfaces. From considerations involving the MoserTrudinger inequality, we characterize some sublevels of the EulerLagrange functional in terms of the topology of the surface and of the data of the equation. This is used together with a minmax argument to obtain existence results.
A variational analysis of the Toda system on compact surfaces
 Comm. Pure Appl. Math
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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. ..."
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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.
A topological degree counting for some Liouville systems of mean field type
 Comm. Pure Appl. Math
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The blow up analysis of solution to the elliptic sinhGordon equation, Calc
 Var. Partical Differential Equations
"... In this paper, we study the blowup analysis of the sinhGordon equation uzz ̄ + λ sinhu = 0, (1) on a 2dimensional surface (Σ, g). This equation plays a very important role in the study of the construction of constant mean curvature surfaces initiated by Wente. ..."
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Cited by 9 (0 self)
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In this paper, we study the blowup analysis of the sinhGordon equation uzz ̄ + λ sinhu = 0, (1) on a 2dimensional surface (Σ, g). This equation plays a very important role in the study of the construction of constant mean curvature surfaces initiated by Wente.
PROFILE OF BUBBLING SOLUTIONS TO A LIOUVILLE SYSTEM
, 2009
"... In several fields of Physics, Chemistry and Ecology, some models are described by Liouville systems. In this article we first prove a uniqueness result for a Liouville system in R 2. Then we establish an uniform estimate for bubbling solutions of a locally defined Liouville system near an isolated ..."
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In several fields of Physics, Chemistry and Ecology, some models are described by Liouville systems. In this article we first prove a uniqueness result for a Liouville system in R 2. Then we establish an uniform estimate for bubbling solutions of a locally defined Liouville system near an isolated blowup point. The uniqueness result, as well as the local uniform estimates are crucial ingredients for obtaining a priori estimate, degree counting formulas and existence results for Liouville systems defined on Riemann surfaces.
Asymptotic Behavior of Blowup Solutions for Elliptic Equations with Exponential Nonlinearity and Singular Data
, 2008
"... We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of BartolucciChenLinTarantello it is proved that the profile of the solutions dif ..."
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Cited by 9 (6 self)
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We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of BartolucciChenLinTarantello it is proved that the profile of the solutions differs from global solutions of a Liouville type equation only by a uniformly bounded term. The present paper improves their result and establishes an expansion of the solutions near the blowup points with a sharp error estimate.
SUPERLIOUVILLE EQUATIONS ON CLOSED RIEMANN SURFACES
, 2005
"... Abstract. Motivated by the supersymmetric extension of Liouville theory in the recent physics literature, we couple the standard Liouville functional with a spinor field term. The resulting functional is conformally invariant. We study geometric and analytic aspects of the resulting EulerLagrange e ..."
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Abstract. Motivated by the supersymmetric extension of Liouville theory in the recent physics literature, we couple the standard Liouville functional with a spinor field term. The resulting functional is conformally invariant. We study geometric and analytic aspects of the resulting EulerLagrange equations, culminating in a blow up analysis. 1.
On Liouville systems at critical parameters, Part 1: One bubble
 J. Funct. Anal
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