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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
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：Introduction to Allard’s regularity theorem（II）
阿拉德 正则性定理 导论
2023/5/17
We continue to discuss the proof of the Allard regularity theorem. In the second presentation, we will focus on the harmonic approximation and the iteration argument for getting the decay of the tilt-...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Introduction to Allard’s regularity theorem（I）
阿拉德 正则性 定理 导论
2023/5/10
In this short seminar, we will discuss the proof of the Allard regularity theorem, which is an $\epsilon$-regularity theorem for the mean curvature equation in the Geometric Measure Theory(GMT) settin...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The regularity with respect to domains of the additive eigenvalues of super-quadratic Hamilton-Jacobi equation
超二次 哈密尔顿-雅可比方程 加性特征值域 规律性
2023/4/27
Viewingtheadditiveeigenvaluesasamapwithrespecttodomainperturbationbyscal- ing, we show that this map enjoys some regularity. Precisely, let c(λ) be the additive eigenvalue with respect to (1 + r(λ))Ω,...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Low regularity conservation laws for the fifth-order modified KdV equations in Besov spaces
Besov空间 五阶修正KdV方程 低正则性 守恒定律
2023/4/19
We get a priori estimates for the fifth-order modified KdV equations in Besov spaces with low regularity which cover the full subcritical range. These estimates are obtained from the power series expa...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An introduction to the Hypergraph Regularity Lemma and its Applications 3
超图 规律性引理 超图正则引理 汉密尔顿循环
2023/4/26
In this talk, we give an example to illustrate how to use the hypergraph regularity lemmas. The absorbing method due to R?dl, Schacht and Szemerédi is a powerful tool in proving hypergraph Hamilton cy...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An introduction to the Hypergraph Regularity Lemma and its Applications 2
超图 规律性引理 超图正则引理 汉密尔顿循环
2023/4/26
In this talk, we first introduce the definitions of equitable partitions and state the hypergraph regularity lemma due to R?dl and Schacht. Then, we give the conception of reduced hypergraphs and its ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An introduction to the Hypergraph Regularity Lemma and its Applications 1
超图 规律性引理 超图正则引理 汉密尔顿循环
2023/4/26
Hypergraph regularity lemmas are generalizations of Szemerédi's regularity lemma for graphs, which has been proved to be a powerful tool with many subsequent. In this talk, we first give a brief intro...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Regularity of sub-elliptic harmonic map into non-positively curved metric space
亚椭圆谐波 非正曲线 度量空间 规律性
2023/4/28
We prove the Holder continuity of a harmonic map from a domain of a sub-Riemannian manifold into a locally compact manifold with non-positive curvature, and more generally into a non-positively curved...
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
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Generic Regularity for All Minimal Hypersurfaces in 8-Manifolds
8流形 最小超曲面 通用规则性
2023/5/5
The well-known Simons cone suggests that singularities may exist in a stable minimal hypersurface in Riemannian manifolds of dimension greater than 7, locally modeled on stable minimal hypercones. It ...
Existence and regularity of extremal solutions for a mean-curvature equation
Mean curvature minimal solution semi-stable solution extremal solution regularity
2015/10/15
We study a class of mean curvature equations −Mu = H +λup where M denotes the mean curvature operator and for p ≥ 1. We show that there exists an extremal parameter λ∗ such that this equat...
REGULARITY OF ABSOLUTELY CONTINUOUS INVARIANT MEASURES FOR PIECEWISE EXPANDING UNIMODAL MAPS
INVARIANT MEASURES UNIMODAL MAPS
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...
A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its L_infinity-norm
Matrix and singular value differentiable function frequency singular value lipschitz second derivative
2015/8/12
The ith singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one. We show that near a local maximum, however, the largest singu...
The Harnack inequality for second-order parabolic equations with divergence-free drifts of low regularity
Harnack inequality second-order parabolic equations divergence-free drifts low regularity
2015/7/14
We establish the Harnack inequality for advection-diffusion equations with divergencefree drifts of low regularity.While our previous work [IKR] considered the elliptic case, here we treat the more ch...