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On a smooth compact manifold of dimensions three and four with totally non-umbilic boundary,imposing non-negativity assumptions on curvatures of the background metric, we establish that there exists a...
We first review some classical results of the Loewner-Nirenberg problem. Then we discuss the characteristics of boundary expansion and its applications in studying the negativity of Ricci curvatures o...
In this talk we will review some recent results on space-time finite and boundary element methods for the wave equation. As a first model problem we consider the inhomogeneous wave equation with zero ...
In this talk, I will discuss the stability conditions for a free boundary problem of compressible Euler equations coupled with a nonlinear Poisson equation of electric potential. Under those stability...
We consider the obstacle problem for a nonlocal elliptic operator, like the integral fractional Laplacian of order $s \in (0,1)$. We derive regularity results in weighted Sobolev spaces, where the wei...
In this talk, the combined quasi-neutral and zero-viscosity limits of the two-fluid Navier-Stokes-Poisson systems (one for ion and another for electron) with boundary are rigorously proved by investig...
In this talk, we mainly show some eigenvalue properties of second order Sturm-Liouville problems and third-order boundary value problems with both transmission conditions and eigenparameter-dependent ...
Free boundary problems have vast and important applications in physics, mechanics, biology, engineering, and finance, etc. At the same time, there is a great challenge in their mathematical study whic...
This conference is the 14th International Conference on Free Boundary Problems: Theory and Applications, which is in the series of conferences beginning in Montecatini (Italy, 1981) and succeeding in ...
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators.
We study the behavior of the Yang-Mills flow for unitary connections on compact and non-compact oriented surfaces with varying metrics. The flow can be used to define a one dimensional foliation on th...
In our previous paper [9], we established a correspondence between vector-valued holomorphic Siegel modular forms and cohomology with local coefficients for local symmetric spaces X attached to real o...
We present a new method for the solution of the unsteady incompressible Navier-Stokes equations. Our goal is to achieve a robust and scalable methodology for two and three dimensional incompressible f...
This article reviews several fast algorithms for boundary integral equations. After a brief introduction of the boundary integral equations for the Laplace and Helmholtz equations, we discuss in order...
We present a high-order boundary integral equation solver for 3D elliptic boundary value problems on domains with smooth boundaries. We use Nystro ¨m’s method for discretization, and combine it with s...

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