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I will give an introduction to Sobolev extensions, including the use of variants of the Whitney extension technique. I will concentrate on the basics of the theory.
We will report Chen-Cheng’s work on cscK equations. We derive the Laplacian bound using Nash-Moser iteration.
We study a class of ultra-parabolic equations, it is a high order degenerate parabolic operators of Hormander type, so it is strongly degenerate, but we prove that this class operators possesses the a...
This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and med...
This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and med...
I will give an introduction to Sobolev extensions, including the use of variants of the Whitney extension technique. I will concentrate on the basics of the theory.
For any θ<1/3 , we show that very weak solutions to the two-dimensional Monge–Ampère equation with regularity C1,θ are dense in the space of continuous functions. This result is shown by a convex inte...
In this talk, we introduce the so-called inverse Lax-Wendroff (ILW) boundary treatment for finite difference approximations on the Cartesian mesh. As the domain boundary may intersect with the grid in...
In this talk, the dispersive revival and fractalization phenomena for bidirectional dispersive equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profile...
Based on the matrix block technique, the Deift-Zhou nonlinear steepest descent method is developed in order to study the asymptotic analysis of solutions of some nonlinear evolution equations associat...
The talk proposes a deep learning method specifically dealing with the forward and inverse problem of variable coefficient partial differential equations-Variable Coefficient Physics-Informed Neural N...
In this talk we relate the Drinfeld half plane studiedso far in the seminar with certain Shimura curves.which are of more global arithmetic interest. Therelation is expressed in a certain uniformizati...
In the study of incompressible fluid, one fundamental phenomenon that arises in a wide variety of application is dissipation enhancement by so-called mixing flow. In this talk, I will give a brief int...
We consider the incompressible Euler equations in two or three dimensions and we show that the addition of a suitable multiplicative It? noise with superlinear growth prevents a smooth solution from b...
Compared to the soliton solutions, the breathers, which are constructed in the mKdV or Gardner equation via integrability methods, are less studied. In our numerical study, we show the interactions be...

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