In this paper we study the ∂-equation with mixed boundary conditions on an annulus Ω = Ω1 \ Ω2 ⊂⊂ C n between two pseudoconvex domains satisfying Ω2 ⊂⊂ Ω1. We prove L-existence theorems for ∂mix for any ∂mix-closed (p, q)-form with 2 ≤ q ≤ n. For the critical case when q = 1 on the annulus Ω, we show that the space of harmonic forms is infinite dimensional and H (p,1) ∂mix,L 2 (Ω) is isomorphic...

In this article, applying different types of boundary conditions; Dirichlet, Neumann, or Mixed, on open strings we realize various new brane bound states in string theory. Calculating their interactions with other D-branes, we find their charge densities and their tension. A novel feature of (p− 2, p) brane bound state is its ”non-commutative” nature which is manifestly seen both in the open st...

In this article we consider open strings with mixed boundary conditions (a combination of Neumann and Dirichlet at each end), and discuss how their end points show a Dp-brane with NS-NS charge, i.e. a bound state of a D-brane with fundamental strings. We show these branes are BPS saturated. Restricting ourselves to D-string case, their mass density is shown to be BPS saturated, in agreement wit...

The variational formulation of the Stokes problem with three independent unknowns, the vorticity, the velocity and the pressure, was born to handle non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We propose an extension of this formulation to the case of mixed boundary conditions in a three-dimensional domain. N...

In this paper we prove that finite element discrete harmonic functions with mixed Dirichlet and Neumann boundary conditions satisfy a weak (Agmon-Miranda) maximum principle on convex polygonal domains. Using this result, we establish the stability of the Ritz projection with mixed boundary conditions in L∞ norm up to a logarithmic term.