Blow up analysis of stationary harmonic maps

2008 ◽  
pp. 87-108
Keyword(s):  
Blow Up ◽  
Harmonic Maps ◽  
Blow Up Analysis

Blow-Up Analysis for Heat Flow of Harmonic Maps

Nematics ◽  
1991 ◽  
pp. 49-64
Author(s):  
Chen Yunmei ◽  
Ding Wei-Yue
Keyword(s):  
Heat Flow ◽  
Blow Up ◽  
Harmonic Maps ◽  
Blow Up Analysis

scholarly journals Regularity and Blow-Up Analysis for J-Holomorphic Maps

2003 ◽  
Vol 05 (04) ◽  
pp. 671-704
Author(s):  
Changyou Wang
Keyword(s):  
Blow Up ◽  
Harmonic Maps ◽  
Hermitian Manifold ◽  
Singular Set ◽  
Holomorphic Maps ◽  
Almost Hermitian Manifold ◽  
Holomorphic Map ◽  
Energy Quantization ◽  
Blow Up Analysis ◽  
Almost Kähler

If u∈H1(M,N) is a weakly J-holomorphic map from a compact without boundary almost hermitian manifold (M,j,g) into another compact without boundary almost hermitian manifold (N,J,h). Then it is smooth near any point x where Du has vanishing Morrey norm ℳ2,2m-2, with 2m= dim (M). Hence H2m-2measure of the singular set for a stationary J-holomorphic map is zero. Blow-up analysis and the energy quantization theorem are established for stationary J-holomorphic maps. Connections between stationary J-holomorphic maps and stationary harmonic maps are given for either almost Kähler manifolds M and N or symmetric ∇hJ.

ON SACKS–UHLENBECK'S EXISTENCE THEOREM FOR HARMONIC MAPS VIA EXPONENTIALLY HARMONIC MAPS

2012 ◽  
Vol 23 (10) ◽  
pp. 1250105 ◽  
Author(s):  
TOSHIAKI OMORI
Keyword(s):  
Existence Theorem ◽  
Homotopy Class ◽  
Existence Result ◽  
Blow Up ◽  
Harmonic Maps ◽  
Closed Surface ◽  
Closed Manifold ◽  
Blow Up Analysis

The blow-up analysis for a sequence of exponentially harmonic maps from a closed surface is studied to reestablish an existence result of harmonic maps from a closed surface into a closed manifold whose 2-dimensional homotopy class vanishes.

BLOW-UP ANALYSIS FOR LIOUVILLE TYPE EQUATION IN SELF-DUAL GAUGE FIELD THEORIES

2005 ◽  
Vol 07 (02) ◽  
pp. 177-205 ◽  
Author(s):  
HIROSHI OHTSUKA ◽  
TAKASHI SUZUKI
Keyword(s):  
Gauge Field ◽  
Blow Up ◽  
Type Equation ◽  
Singular Part ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Liouville Type ◽  
Blow Up Analysis ◽  
The Green Function ◽  
Dirac Measures

We study the asymptotic behavior of the solution sequence of Liouville type equations observed in various self-dual gauge field theories. First, we show that such a sequence converges to a measure with a singular part that consists of Dirac measures if it is not compact in W1,2. Then, under an additional condition, the singular limit is specified by the method of symmetrization of the Green function.

scholarly journals Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Bo Fang ◽  
Yan Chai
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Quasilinear Parabolic Equation ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Blow Up Analysis ◽  
Inner Absorption ◽  
Quasilinear Parabolic

We investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee thatu(x,t)exists globally or blows up at some finite timet*. Moreover, an upper bound fort*is derived. Under somewhat more restrictive conditions, a lower bound fort*is also obtained.

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