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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：Multiple solutions for a Kirchhoff-type fractional coupled problem with p-Laplacian
p-Laplacian算子 Kirchhoff型分数 耦合问题 多重解
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2023/11/13
We discuss a class of two-parameters coupled Kirchhoff-type fractional differential equations. Two differentiated methods are used to prove the existence of two solutions to the equation. The fundamen...
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators
Harmonic function boundary Harnack principle gradient estimate
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2016/1/20
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators.
Random Homogenization of Fractional Obstacle Problems
Random Homogenization Fractional Obstacle Problems
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2015/10/15
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.
Fractional diffusion limit for collisional kinetic equations
fractional diffusion fractional heat equation anomalous heat transport linear Boltzmann equation relaxation equation linear BGK equation diffusion limit anomalous diffusion limit anomalous diffusive time scale mathematical derivation
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2015/10/15
This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, t...
Fractional diffusion limit for collisional kinetic equations:A moments method
Kinetic equations linear Boltzmann equation asymptotic analysis diffusion limit anomalous diffusion limit fractional diffusion relaxation equation anomalous diffusive time scale
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2015/10/15
This paper is devoted to hydrodynamic limits of linear kinetic equations. We consider situations in which the thermodynamical equilibrium is described by a heavy-tail distribution function rather than...
Fractional diffusion limit for collisional kinetic equations:a Hilbert expansion approach
Fractional diffusion limit collisional kinetic equations Hilbert expansion
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2015/10/15
We develop a Hilbert expansion approach for the derivation of fractional diffusion equations from the linear Boltzmann equation with heavy tail equilibria.
Homogenization driven by a fractional Brownian motion:the shear layer case
Homogenization driven fractional Brownian motion shear layer case
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2015/7/14
We consider a passive scalar in a periodic shear flow perturbed by an additive fractional noise with the Hurst exponent H ∈ (0, 1). We establish a diffusive homogenization limit for the tracer when th...
Construction of fractional factorial split-plot designs with weak minimum aberration
fractional factorial split-plot designs weak minimum aberration
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2015/3/20
Construction of fractional factorial split-plot designs with weak minimum aberration.
Fractional Factorial Designs With Admissible Sets of Clear Two-Factor Interactions
Fractional Factorial Designs Admissible Sets Clear Two-Factor Interactions
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2015/3/20
Fractional Factorial Designs With Admissible Sets of Clear Two-Factor Interactions.
Fractional Analytic Index
Fractional Analytic Index
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2015/3/19
Fractional Analytic Index.
The role of Chern Simons theory in solving the fractional quantum Hall effect mystery
Chern Simons theory fractional quantum Hall effect
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2015/3/19
The role of Chern Simons theory in solving the fractional quantum Hall effect mystery.
Construction of fractional factorial split-plot designs with weak minimum aberration
Factorial design Split-plot Weak minimum aberration
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2015/3/18
Fractional factorial split-plot (FFSP) designs with minimum aberration have received
much attention in industrial experiments. But they are not so easy to be constructed for the
cases when there are...
Fractional Laplacian in conformal geometry
Conformal geometry Fractional Laplacian Conformally covariant operators Dirichlet-to-Neumann operators Asymptotically hyperbolic manifolds
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2014/4/3
In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli and Silvestre and a class of conformally covariant operators in conformal...
Boundary Value Problems for Differential Equations of Fractional Order
Boundary Value Problems Fractional Order
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2012/8/10
We carry out spectral analysis of one class of integral op-
erators associated with fractional order differential equations that arise in
mechanics. We establish a connection between the eigenvalues...