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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...
Consider a point mass falling vertically on an infinitely heavy
horizontal plate which oscillates periodically with period 2π in the vertical direction
and interacts with the particle by the l...
DIFFERENTIAL HARNACK ESTIMATES FOR TIME-DEPENDENT HEAT EQUATIONS WITH POTENTIALS
EQUATIONS WITH POTENTIALS DIFFERENTIAL HARNACK
2015/8/17
In this paper, we prove a differential Harnack inequality for positive
solutions of time-dependent heat equations with potentials. We also prove a gradient
estimate for the positive solution o...
DIFFERENTIAL HARNACK ESTIMATES FOR BACKWARD HEAT EQUATIONS WITH POTENTIALS UNDER THE RICCI FLOW
HARNACK ESTIMATES WITH POTENTIALS UNDER THE RICCI FLOW
2015/8/17
In this paper, we derive a general evolution formula for possible Harnack quantities. As a consequence, we prove several differential Harnack inequalities
for positive solutions of backward hea...
Existence, Stability, and Dynamics of Solitary Waves in Nonlinear Schroedinger Models with Periodic Potentials
Non-square lattices, Nonlinear waves Photonic lattices
2014/12/8
The focus of this dissertation is the existence, stability, and resulting dynamical evolution of localized stationary solutions to Nonlinear Schr¨odinger (NLS) equations with periodic confining potent...
Soliton dynamics of NLS with singular potentials
Nonlinear Schrodinger equation soliton dynamics singular potentials
2012/6/30
We investigate the validity of a soliton dynamics behavior in the semi-relativistic limit for the nonlinear Schr\"odinger equation in $\R^{N}, N\ge 3$, in presence of a singular external potential.
Quivers with potentials associated to triangulated surfaces, part IV: Removing boundary assumptions
Quivers potentials triangulated surfaces Removing boundary assumptions Combinatorics
2012/6/30
We prove that the quivers with potentials associated by the author to ideal triangulations of punctured surfaces with empty boundary are non-degenerate, provided the number of punctures is 1 or greate...
Liouville-Arnold integrability for scattering under cone potentials
Liouville-Arnold integrability scattering cone potentials Dynamical Systems
2012/4/26
The problem of scattering of particles on the line with repulsive interactions, gives rise to some well-known integrable Hamiltonian systems, for example, the nonperiodic Toda lattice or Calogero's sy...
Reducing scattering problems under cone potentials to normal form by global canonical transformations
scattering problems cone normal form global canonical transformations Exactly Solvable and Integrable Systems
2012/4/26
We introduce a class of Hamiltonian scattering systems which can be reduced to the "normal form" $\dot P=0$, $\dot Q=P$, by means of a global canonical transformation $ (P,Q)=A(p,q), p,q\in R^n$, defi...
An O(N) Method for Rapidly Computing Periodic Potentials Using Accelerated Cartesian Expansions
Accelerated Cartesian Expansion (ACE) Fast Multipole Methods Periodic Systems
2011/10/8
Abstract: The evaluation of long-range potentials in periodic, many-body systems arises as a necessary step in the numerical modeling of a multitude of interesting physical problems. Direct evaluation...
Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half-harmonic maps
Harmonic maps nonlinear elliptic PDE’s regularity of solutions
2011/1/20
We consider nonlocal linear Schr¨odinger-type critical systems of the type 1/4v = v in IR. (1) where is antisymmetric potential in L2(IR, so(m)), v is a IRm valued map and
v denotes the matrix mu...
Singular operators with antisymmetric kernels, related capacities, and Wolff potentials
Singular operators antisymmetric kernels related capacities Wolff potentials
2011/1/21
We consider a generalization of the Riesz operator in Rd and obtain estimates for its norm and for related capacities via the modified Wolff potential. These estimates are based on the certain version...
Lipschitz-continuity of the integrated density of states for Gaussian random potentials
Lipschitz-continuity integrated density states for Gaussian random potentials
2011/1/17
The integrated density of states of a Schr¨odinger operator with random potential given by a homogeneous Gaussian field whose covariance function is continuous, compactly supported and has positive me...
On a relation between potentials for pluriharmonic maps and para-pluriharmonic maps
potential pluriharmonic map para-pluriharmonic map the loop group
2011/1/17
In this paper, we show that one can interrelate pluriharmonic maps with para-pluriharmonic maps by means of the loop group method. As an appendix, we give examples for the interrelation between plurih...
Supersymmetry transformations for singular potentials
Supersymmetry transformations singular potentials
2011/3/2
Wemake a detailed study of the first and second-order SUSYpartners of a one-dimensional free Hamiltonian with a singular perturbation proportional to a Dirac delta function. It is shown that the secon...