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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Bubbling and extinction for some fast diffusion equations in bounded domains
有界域 快速扩散方程 气泡 消光
2023/11/13
Motivated by the Wisconsin octupole experiments on anomalous diffusion of hydrogen plasma across a purely poloidal octupole magnetic field, Berryman-Holland 1980 proved the stability of separable solu...
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：Bergman reproducing kernels for nearly holomorphic functions on bounded symmetric domains
伯格曼 有界对称域 近乎全纯函数 核
2023/4/17
Nearly holomorphic functions on symmetric domains are defined by Shimura as polynomial of differential of Kaehler potential with holomorphic coefficients. We find the corresponding Bergman reproducing...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Bergman reproducing kernels for nearly holomorphic functions on bounded symmetric domains
伯格曼 有界对称域 近乎全纯函数 核
2023/4/23
Nearly holomorphic functions on symmetric domains are defined by Shimura as polynomial of differential of Kaehler potential with holomorphic coefficients. We find the corresponding Bergman reproducing...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rigidity of non-compact static domains in hyperbolic space via positive mass theorems
正质量定理 双曲空间 非紧致 静域刚性
2023/4/14
We single out a notion of staticity which applies to any domain in hyperbolic space whose boundary is a non-compact totally umbilical hypersurface. For (time-symmetric) initial data sets modeled at in...
A PROOF OF THE UNIFORMIZATION THEOREM FOR ARBITRARY PLANE DOMAINS
UNIFORMIZATION THEOREM ARBITRARY PLANE DOMAINS
2015/8/26
We present a simple constructive proof of the Uniformization Theorem which works for plane domains. The proof is a combination of covering space theory and Koebe's constructive proof of the Riemann ma...
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
oundary integral equations Nystrom discretization Singular integrals Nearly singular integrals Fast solvers Laplace equation Stokes equation Navier equation Fast multipole method Fast Fourier transform
2015/7/14
We present a high-order boundary integral equation solver for 3D elliptic boundary value problems on domains with smooth boundaries. We use Nystro ¨m’s method for discretization, and combine it with s...
Geometric Analysis for the Metropolis Algorithm on Lipschitz Domains
Geometry comparison Steve Nash sobolev inequality the convergence rate
2015/7/7
This paper gives geometric tools: comparison, Nash and Sobolev inequalities for pieces of the relevent Markov operators, that give useful bounds on rates of convergence for the Metropolis algorithm. A...
Semi-linear equations and principal eigenvalues in unbounded domains
Semi-linear equations principal eigenvalues unbounded domains
2015/4/3
Semi-linear equations and principal eigenvalues in unbounded domains.
Iteration theory of Maslov-type index associated with a Lagrangian subspace for symplectic paths and Multiplicity of brake orbits in bounded convex symmetric domains
Iteration theory Maslov-type index Lagrangian subspace symplectic paths and Multiplicity brake orbits in bounded convex symmetric domains
2015/4/3
Iteration theory of Maslov-type index associated with a Lagrangian subspace for symplectic paths and Multiplicity of brake orbits in bounded convex symmetric domains.
D-bar and Dirac Type Operators on Classical and Quantum Domains
Dirac Operators Noncommutative Geometry
2015/1/19
I study d-bar and Dirac operators on classical and quantum domains subject to the APS boundary conditions, APS like boundary conditions, and other types of global boundary conditions. Moreover, the in...
Initial-irregular oblique derivative problem for nonlinear parabolic equations of second order in multiply connected domains
Initial-irregular oblique derivative problem nonlinear parabolic equa-tions multiply connected domains
2014/9/26
n this article, we discuss that an initial-irregular oblique derivative problem for non-linear uniformly parabolic complex equation of second order
A0
u
zˉ z −Re[Quzz+A1
u
z
]−A2
u&...
The approximate method of irregular oblique derivative problem for nonlinear elliptic equa-tions in multiply connected infinite domains
Approximate method irregular oblique derivative problem nonlinear elliptic equations multiply connected infinite domains
2014/9/26
n this article, we discuss the approximate method of solving irregular
oblique derivative problem for nonlinear uniformly elliptic equation of second order
u
z1 z =F(z; u; u
z
; u
zz
) in D; (0...
The oblique derivative problem for nonlinear elliptic complex equations of second order in multiply connected unbounded domains
Oblique derivative problem nonlinear elliptic complex equations multiply connected unbounded domains
2014/9/26
In this article, we discuss that an oblique derivative boundary value problem for
nonlinear uniformly elliptic complex equation of second order
wz1z=F(z; w; w
z
;wz; w
zz
;wzz)+G(z; w; ; w
z
;...
The Discontinuous Riemann-Hilbert problem for analytic functions in multiply connected domains
Discontinuous Riemann-Hilbert problems analytic functions A priori estimates and existence of solutions
2014/9/26
In [2], the authors introduce the Keldych-Sedov formula for analytic
functions in the upper half-plane, namely the representation of solutions of the mixed
boundary value problem for analytic functi...