Singular perturbation problems have been studied by many mathematicians. Since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. This paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

In the paper, we establish existence of steady boundary layer solution Boltzmann equation with specular condition in L 2 ∩L ∞ half-space. The uniqueness, continuity and exponential decay are obtained, such estimates important to prove Hilbert expansion for half-space problem condition.

We show that on an open bounded smooth strongly pseudoconvex subset of C, there exists a Kähler-Einstein metric with positive Einstein constant, such that the metric restricted to the Levi distribution of the boundary is conformal to the Levi form. To achieve this, we solve an associated complex Monge-Ampère equation with Dirichlet boundary condition. We also prove uniqueness under some more as...

We study fermions, such as gravitinos and gauginos in supersymmetric theories, propagating in a five-dimensional bulk where the fifth dimensional component is assumed to be an interval. We show that the most general boundary condition at each endpoint of the interval is encoded in a single complex parameter representing a point in the Riemann sphere. Upon introducing a boundary mass term, the v...

In this paper, using the boundary properties of the analytic functions we investigate the structure of the discrete spectrum of the boundary value problem iy 1 + q1(x)y2 − λy1 = φ1(x) (0.1) −iy 2 + q2(x)y1 − λy2 = φ2(x), x ∈ R+ and the condition (a1λ+ b1)y2(0, λ)− (a2λ+ b2)y1(0, λ) = 0 (0.2) where q1, q2, φ1, φ2 are complex valued functions, ak 6= 0, bk 6= 0 , k = 1, 2 are complex constants and...

Several abstract model problems of elliptic and parabolic type with inhomogeneous initial and boundary data are discussed. By means of a variant of the Dore-Venni theorem, real and complex interpolation, and trace theorems, optimal Lp-regularity is shown. By means of this purely operator theoretic approach, classical results on Lp-regularity of the diffusion equation with inhomogeneous Dirichle...

The classical Oka’s Lemma states that if Ω is a pseudoconvex domain in C, n ≥ 2, then − log δ is plurisubharmonic where δ is some distance function to the boundary. Let M be a complex hermitian manifold with the metric form ω. Let Ω be relatively compact pseudoconvex domain in M . We say that a distance function δ to the boundary bΩ satisfies the strong Oka condition if it can be extended from ...