Related papers: On regularity of a Kinetic Boundary layer
We consider an overdetermined problem for a two phase elliptic operator in divergence form with piecewise constant coefficients. We look for domains such that the solution $u$ of a Dirichlet boundary value problem also satisfies the…
We propose a necessary and sufficient condition for the well-posedness of the linear non-homogeneous Grad moment equations in half-space. The Grad moment system is based on Hermite expansion and regarded as an efficient reduction model of…
We study the boundary layer solution to singular perturbation problems involving Poisson-Boltzmann (PB) type equations with a small parameter $\epsilon$ in general bounded smooth domains (including multiply connected domains) under the…
In this paper, we study the full regularity and well-posedness of classical solutions to the nonlinear unsteady Prandtl equations with Robin or Dirichlet boundary condition in half space. Under Oleinik's monotonicity assumption, we prove…
This article proves the regularity for the Boltzmann equation without angular cutoff with hard potential. By sharpening the coercivity and upper bound estimate on the collision operator, analyzing the Poisson bracket between the transport…
The $P_1$--nonconforming quadrilateral finite element space with periodic boundary condition is investigated. The dimension and basis for the space are characterized with the concept of minimally essential discrete boundary conditions. We…
We study the boundary regularity of solutions to the porous medium equation $u_t = \Delta u^m$ in the degenerate range $m>1$. In particular, we show that in cylinders the Dirichlet problem with positive continuous boundary data on the…
We introduce a new constructive method for establishing lower bounds on convergence rates of periodic homogenization problems associated with divergence type elliptic operators. The construction is applied in two settings. First, we show…
In this paper, we establish $C^{1, \alpha}$ regularity upto the boundary for a class of degenerate fully nonlinear elliptic equations with Neumann boundary conditions. Our main result Theorem 2.1 constitutes the boundary analogue of the…
This paper considers the neutron transport equation in bounded domain with a combination of the diffusive boundary condition and the in-flow boundary condition. We firstly study the existence of solution in any fixed time by…
We consider a quasilinear equation given in the half-space, i.e. a so called boundary reaction problem. Our concerns are a geometric Poincar\'e inequality and, as a byproduct of this inequality, a result on the symmetry of low-dimensional…
We study periodic homogenization problems for second-order pde in half-space type domains with Neumann boundary conditions. In particular, we are interested in "singular problems" for which it is necessary to determine both the homogenized…
Let $\Omega$ be a Lipschitz domain in $\mathbb R^n$ $n\geq 2,$ and $L=\mbox{div} (A\nabla\cdot)$ be a second order elliptic operator in divergence form. We establish solvability of the Dirichlet regularity problem with boundary data in…
This paper is concerned with the asymptotic stability of planar stationary solution to an initial-boundary value problem for a two-dimensional hyperbolic-elliptic coupled system of the radiating gas in half space. We show that the solution…
The paper proves existence of renormalized stationary solutions for a dense class of discrete velocity Boltzmann equations in the plane with given ingoing boundary values. The proof is based on the construction of a sequence of…
A dilute gas of hard disks confined between two straight parallel lines is considered. The distance between the two boundaries is in between one and two particle diameters, so that the system is quasi-one-dimensional. A Boltzmann-like…
In this article we establish fine results on the boundary behavior of solutions to nonlocal equations in $C^{k,\gamma}$ domains which satisfy local Neumann conditions on the boundary. Such solutions typically blow up at the boundary like $v…
We prove localized energy estimates for the wave equation in domains with a strictly concave boundary when homogeneous Dirichlet or Neumann conditions are imposed. By restricting the solution to small, frequency dependent, space time…
We introduce a Bergman-space framework for the study of boundary-forced heat equations and show that, in the one-dimensional case, boundary white noise gives rise to a sharp holomorphic regularity phenomenon. More precisely, we consider the…
A fully non-linear kinetic Boltzmann equation for anyons and large initial data is studied in a periodic 1d setting. Strong L1 solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness, and…