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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：C1,1/3- very weak solutions to the two dimensional Monge–Ampère equation
二维 Monge–Ampère方程 C1,1/3极弱解
2023/11/29
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...
Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions
Local-in-space estimates initial time weak solutions of the Navier-Stokes equations forward self-similar solutions Analysis of PDEs
2012/4/18
We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with $(-1)$-homogeneous initial data has a global scale-invariant solution which is smooth for positive time...
On the existence of weak solutions to the three-dimensional steady compressible Navier-Stokes equations in bounded domains
Steady compressible Navier-Stokes equations existence for any γ > 1 weighted estimate bounded domains
2011/9/22
Abstract: We prove the existence of a weak solution to the three-dimensional steady compressible isentropic Navier-Stokes equations in bounded domains for any specific heat ratio \gamma > 1. Generally...
High order weak approximation schemes for Lévy-driven SDEs
Levy-driven stochastic di erential equation Euler scheme
2011/2/28
We propose new jump-adapted weak approximation schemes for stochas-tic di erential equations driven by pure-jump Levy processes.
Weak Maximum Principle for Strongly Coupled Elliptic Differential Systems
Weak maximum principle strongly coupled elliptic system weak solution
2010/12/10
A classical counterexample due to E. De Giorgi, shows that the weak maximum principle
does not remain true for general linear elliptic differential systems. After that, there are some efforts to esta...
Weak solutions to lubrication equations in the presence of strong slippage
Weak solutions lubrication equations presence of strong slippage
2011/1/18
The existence of global weak solutions is proved for one-dimensional lubrication models that describe the dewetting process of nanoscopic thin polymer films on hy-drophobyzed substrates and take accou...
H¨older continuity of the weak solutions for parabolic equations with the nonstandard growth condition
Boundedness H\
2007/12/12
In this paper, we investigate the interior regularity including the local boundedness and the interior H\"{o}lder continuity of weak solutions for parabolic equations of the $p(x,t)$-Laplacian type. W...