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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...
We present an explicit two-parameter family of finite-band Jacobi elliptic potentials given by $q\equiv A\dn(x;m)$, where $m\in(0,1)$ and $A$ can be taken to be positive without loss of generality, fo...
A locally optimal preconditioned Newton-Schur method is proposed for solving symmetric elliptic eigenvalue problems. Firstly, the Steklov-Poincaré operator is used to project the eigenvalue problem on...
Legendre Pairs are combinatorial objects with a rich 20+ years history. Their main application is that they furnish a structured form of the Hadamard conjecture and they have been studied by several a...
In this talk, I will describe an elliptic PDE that models electric conduction, and the electric field concentration phenomenon between closely spaced inclusions of high contrast. In the first part, I ...
Equidistribution is an important theme in number theory. The Sato-Tate conjecture, which was established by Richard Taylor et.al. in 2008, asserts that given an elliptic curve over Q without complex m...
简介椭圆型方程正则性的基本结果,综述弱正则数据下其方程解的Calderon-Zygmund估计和Schauder估计的基本方法和近期进展,分析非线性椭圆方程组的部分正则性和处处正则问题,介绍我们在有关问题上的一些研究。
简介椭圆型方程正则性的基本结果,综述弱正则数据下其方程解的Calderon-Zygmund估计和Schauder估计的基本方法和近期进展,分析非线性椭圆方程组的部分正则性和处处正则问题,介绍我们在有关问题上的一些研究。
We study a Monge-Ampère type equation which interpolates the sigma_2-Yamabe equation in conformal geometry and the 2-Hessian equation. In dimension 4, we prove a corresponding Liouville’s theorem. Our...
Quasi-elliptic cohomology is closely related to Tate K-theory. It is constructed as an object both reflecting the geometric nature of elliptic curves and more practicable to study than most elliptic c...
An elliptic cohomology theory is an even periodic multiplicative generalized cohomology theory whose associated formal group is the formal completion of an elliptic curve. It is at the intersection of...
In this paper, a posteriori error estimate of a weak Galerkin (WG) finite element method for solving H(curl)-elliptic problems is designed and analyzed. Firstly, a WG method for H(curl)-elliptic probl...
The regularity estimates have well-established for second-order elliptic and parabolic equations, as well as for equations with stable-like non-local operators. Whether similar results hold for non-lo...
We prove the Holder continuity of a harmonic map from a domain of a sub-Riemannian manifold into a locally compact manifold with non-positive curvature, and more generally into a non-positively curved...

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