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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonlinear potentials at the fractional scale:sharp regularity
分数尺度 非线性势 尖锐 正则性
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2023/11/29
Nonlinear potential theory and elliptic regularity theory are two classical topics in the modern analysis of partial differential equations. In this talk I show how these themes merge to solve the lon...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Critical Allard regularity in dimension two and its application
二维中临界 阿拉德规律性 欧几里得空间
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2023/5/5
The classical Allard regularity says, a rectifiable varifold in the unit ball of the Euclidean space passing through the original point with volume density close to 1 and generalized mean curvature sm...
REGULARITY OF ABSOLUTELY CONTINUOUS INVARIANT MEASURES FOR PIECEWISE EXPANDING UNIMODAL MAPS
INVARIANT MEASURES UNIMODAL MAPS
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2015/9/29
An important discovery of the 20th century mathematics is that many deterministic
systems exhibit stochastic behavior. The stochasticity is caused by exponential divergence of nearby trajectories. Th...
NOTE ON GLOBAL REGULARITY FOR 2D OLDROYD-B FLUIDS WITH DIFFUSIVE STRESS
Oldroyd-B, complex uids Fokker-Planck equations blow up global existence Euler equations Navier-Stokes equations kinetic equations
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2014/4/3
We prove global regularity of solutions of Oldroyd-B equations in 2 spatial dimensions with spatial di usion of the polymeric stresses.
New logarithmic Sobolev inequalities and an ε-regularity theorem for the Ricci flow
New logarithmic Sobolev inequalities ε-regularity theorem Ricci flow Differential Geometry
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2012/5/24
In this note we prove a new \epsilon-regularity theorem for the Ricci flow. Let (M^n,g(t)) with t\in [-T,0] be a Ricci flow and H_{x} the conjugate heat kernel centered at a point (x,0) in the final t...
Interior partial regularity for minimal Lp-vectorfields with integer fluxes
Interior partial regularity minimal Lp-vectorfields integer fluxes
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2012/4/17
We use a new combinatorial technique to prove the optimal interior partial regularity result for Lp-vectorfields with integer fluxes minimizing the Lp-energy. More precisely, we prove that the minimal...
Quantitative Stratification and the Regularity of Harmonic Maps and Minimal Currents
Quantitative Stratification the Regularity of Harmonic Maps Minimal Currents
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2011/9/9
Abstract: We introduce techniques for turning estimates on the infinitesimal behavior of solutions to nonlinear equations (statements concerning tangent cones and blow ups) into more effective control...
Five lectures on optimal transportation: Geometry, regularity and applications
optimal transportation Geometry regularity applications
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2010/11/19
In this series of lectures we introduce the Monge-Kantorovich problem of optimally transporting one distribution of mass onto another, where optimality is measured against a cost function c(x,y). Con...
Weighted Bergman Projections and Kernels: Lp Regularity and Zeros
Weighted Bergman Projections Kernels: Lp Regularity Zeros
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2010/12/6
We investigate Lp regularity of weighted Bergman projec-tions and zeros of weighted Bergman kernels for the weights that are radially symmetric and comparable to 1 on the unit disc.