Let $\Omega$ be an unbounded two dimensional strip on a ruled surface in $\mathbb{R}^d$, $d\geq2$. Consider $-\Delta_{\Omega}^{D}$ the Dirichlet Laplacian operator restricted to $\Omega$ and $-\Delta_{\Omega}^{DN}$ the ...

We obtain a necessary and sufficient condition in order that a semi-plane of the form R(s) > r, r is an element of R, is free of zeros of a given Dirichlet polynomial. The result may be considered a natural generalisation ...

In this work, we study existence and non existence for the Dirichlet problem for the minimal graph equation in non convex domains of the plane. We search for conditions on the boundary data which be the less restricted ...

ADER schemes are numerical methods, which can reach an arbitrary order of accuracy in both space and time. They are based on a reconstruction procedure and the solution of generalized Riemann problems. However, for general ...

Let $\Omega_\varepsilon$ be a thin strip in $\mathbb{R}^2$ and $-\Delta_{DN}^{\Omega_\varepsilon}$ the Dirichlet-Neumann Laplacian in $\Omega_\varepsilon$. In this work, we study the spectral problem of $-\Delta_{DN}^{\O ...

Let be a polygonal domain in R2 and let U be a weak solution of u = f in with Dirichlet boundary condition, where f 2 Lp !( ) and ! is a weight in Ap(R2), 1 < p < 1. We give some estimates of the Green function ...