We establish sharp boundary regularity estimates in C and C domains for nonlocal problems of the form Lu = f in Ω, u = 0 in Ω. Here, L is a nonlocal elliptic operator of order 2s, with s ∈ (0, 1). First, in C domains we show that all solutions u are C up to the boundary and that u/d ∈ C(Ω), where d is the distance to ∂Ω. In C domains, solutions are in general not comparable to d, and we prove a...

The flow in an enclosed completely filled rapidly rotating cylinder that is driven by the differential corotation of the top lid is studied numerically. Although the flow is in a very simple geometry, the fast background rotation and large differential rotation of the lid lead to very thin boundary layers with a variety of instability modes with very fine spatial scales as well as inertial wave...

Instabilities of nonlinear waves on unbounded domains manifest themselves in different ways. An absolute instability occurs if the amplitude of localized wave packets grows in time at each fixed point in the domain. In contrast, convective instabilities are characterized by the fact that even though the overall norm of wave packets grows in time, perturbations decay locally at each given point ...

Contents 1 Introduction 2 2 The Dirichlet problem and the boundary trace 7 2. Abstract We study the boundary value problem with measures for (E1) −∆u + g(|∇u|) = 0 in a bounded domain Ω in R N , satisfying (E2) u = µ on ∂Ω and prove that if g ∈ L 1 (1, ∞; t −(2N +1)/N dt) is nondecreasing (E1)-(E2) can be solved with any positive bounded measure. When g(r) ≥ r q with q > 1 we prove that any pos...

Consider the large systems of linear equations A h u h = f h which arise from the discretization of a second-order elliptic boundary value problem. Consider also the preconditioned systems (i) Bh − 1 A h u h = Bh 1 f h; and (ii) A h Bh 1 v h = f h , u h = Bh 1 v h where B h is itself a matrix which arises from the discretization of another elliptic operator. We discuss the effect of boundary co...

The escape structure in southwest Taiwan has long been discussed. counterclockwise rotation GPS ground motion is argued to be evidence of tectonic escape. However, events worldwide are always bounded by lithosphere-cutting strike-slip faults at the boundary lithospheric-scale rotating block, and these have not observed Taiwan. In this study, we propose that a thin-skinned deformation due open c...

For solutions to the capillarity problem possibly with the boundary contact angle θ being 0 and/or π in a relatively open portion of the boundary which is C2, we will show that if the solution is locally bounded up to this portion of boundary, the trace of the solution on this portion is piecewise Lipschitz continuous and the solution is Hölder continuous up to the boundary, provided the prescr...

Effect of a toroidal rotation on the type-I edge localized mode in JT-60U is investigated numerically. As the result of the numerical analysis, it is confirmed that the plasma rotating experimentally in the co-direction to the plasma current is approximately on the stability boundary of the MHD mode even when the rotation is neglected. However, the plasma rotating in the counter-direction is fa...

Let Ω be a connected bounded domain with a finite amount of “holes” and “nice boundary”. We study subnormal operators with spectrum equal to Ω, while the spectrum of their normal extensions are supported on the boundary, ∂Ω.