Related papers: Arguments towards the construction of a matrix mod…
We consider natural conformal invariants arising from the Gauss-Bonnet formulas on manifolds with boundary, and study conformal deformation problems associated to them. The key technique we used is to derive boundary C^2 estimates directly…
We study the boundary value problem for the stationary Navier--Stokes system in two dimensional exterior domain. We prove that any solution of this problem with finite Dirichlet integral is uniformly bounded. Also we prove the existence…
We construct a frame of complex Gaussians for the space of $L^2(\mathbb{R}^n)$ functions. When propagated along bicharacteristics for the wave equation, the frame can be used to build a parametrix with suitable error terms. When the…
We consider the Maxwell's equations with perfect electric conductor boundary conditions in three-dimensional unbounded domains which are the union of a bounded resonator and one or several semi-infinite waveguides. We are interested in the…
In this paper, we investigate a system composed of two degenerate wave equations which are connected at one point. By introducing some inequalities on the weighted spaces and employing the frequency domain method, we prove that the system…
We study the ground state of the boundary Izergin-Korepin model. The boundary Izergin-Korepin model is defined by so-called $R$-matrix and $K$-matrix for $U_q(A_2^{(2)})$ which satisfy Yang-Baxter equation and boundary Yang-Baxter equation…
Consider 3D Boltzmann equation in convex domains with diffusive-reflection boundary condition. We study the hydrodynamic limits as the Knudsen number and Strouhal number $\epsilon\rightarrow 0^+$. Using the Hilbert expansion, we rigorously…
We consider weighted p-Laplace type equations with homogeneous Neumann boundary conditions in convex domains, where the weight is a log-concave function which may degenerate at the boundary. In the case of bounded domains, we provide sharp…
A prominent class of model FQH ground states is those realized as correlation functions of $\mathbb{Z}_k^{(r)}$-algebras. In this paper, we study the interplay between these algebras and their corresponding wavefunctions. In the hopes of…
We establish a Fatou-type Theorem for $J$-holomorphic mappings that are bounded in an appropriate sense and we prove the Blaschke condition for their zero sets. We also prove a Privalov-type uniqueness Theorem for pairs of $J$-holomorphic…
This paper is concerned with the Boltzmann equation with specular reflection boundary condition. We construct a unique global solution and obtain its large time asymptotic behavior in the case that the initial data is close enough to a…
We study a wide class of linear inhomogeneous boundary-value problems for $r$th order ODE-systems depending on a parameter $\mu$ in a general metric space $\mathcal M$. The solutions belong to the Sobolev spaces $(W^{n+r}_p)^m$,…
We address various issues concerning the Cauchy problem for the Zakharov-Rubenchik system (known as the Benney-Roskes system in water waves theory), which models the interaction of short and long waves in many physical situations. Motivated…
This paper is devoted to the study of the inhomogeneous wave equation with singular (less than continuous) time dependent coefficients. Particular attention is given to the role of the lower order terms and suitable Levi conditions are…
We study the consequences of the presence of a boundary in topological field theories in various dimensions. We characterize, univocally and on very general grounds, the field content and the symmetries of the actions which live on the…
The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Under the assumption that the vorticity is a negative constant whose absolute value is sufficiently large, we…
We generalize the twisted quantum double model of topological orders in two dimensions to the case with boundaries by systematically constructing the boundary Hamiltonians. Given the bulk Hamiltonian defined by a gauge group $G$ and a…
The object of this paper is twofold. Firstly, we study a class of generalized Newtonian fluid related to "power law ". For the corresponding non-Newtonian Navier-Stokes problems, the existence of a weak and periodic solutions is proved in…
We study second-order divergence-form systems on half-infinite cylindrical domains with a bounded and possibly rough base, subject to homogeneous mixed boundary conditions on the lateral boundary and square integrable Dirichlet, Neumann, or…
In the framework of scattering theory, we show how the scattering matrix can be related to the projection on the bound states by an index map of K-theory. Pairings with appropriate cyclic cocyles lead naturally to a topological version of…