The positivity-preserving property for the inverse of the biharmonic operator under Steklov boundary conditions is studied. It is shown that this property is quite sensitive to the parameter involved in the boundary condition. Moreover, positivity of the Steklov boundary value problem is linked with positivity under boundary conditions of Navier and Dirichlet type.

In the past few years, different models and analytical approximations have been developed facing the problem of the electrical conductivity of a concentrated colloidal suspension, according to the cell-model concept. Most of them make use of the Kuwabara cell model to account for hydrodynamic particle-particle interactions, but they differ in the choice of electrostatic boundary conditions at t...

In the context of a symmetric diffusion process X admitting a carré du champs operator, we give a precise description of the Dirichlet form of the process obtained by subjecting X to a drift transformation of gradient type. This description relies on boundary-type conditions restricting an associated reflecting Dirichlet form.

We consider the stabilization of the wave equation with space variable coefficients in a bounded region with a smooth boundary, subject to Dirichlet boundary conditions on one part of the boundary and linear or nonlinear dissipative boundary conditions of memory type on the remainder part of the boundary. Our stabilization results are mainly based on the use of differential geometry arguments, ...

By means of a Picone’s type identity, we prove uniqueness and oscillation of solutions to an elliptic semilinear equation with Dirichlet boundary conditions.

A fourth-order accurate embedded boundary method for the scalar wave equation with Dirichlet or Neumann boundary conditions is described. The method is based on a compact Pade-type discretization of spatial derivatives together with a Taylor series method (modified equation) in time. A novel approach for enforcing boundary conditions is introduced which uses interior boundary points instead of ...

We use a numerical-analytic technique to construct sequence of successive approximations the solution system fractional differential equations, subject Dirichlet boundary conditions. prove uniform convergence limit function, which is unique value problem under consideration, and give necessary sufficient conditions for existence solutions. The obtained theoretical results are confirmed by model...

We study general 2nd order fully nonlinear degenerate elliptic equations on an arbitrary closed set with generalized Dirichlet boundary conditions in the viscosity sense. We prove some properties of the maximal subsolution and the minimal supersolution of the Dirichlet type problem. Under a sort of compatibility condition on the boundary data we show that the maximal subsolution is the natural ...