In this paper, we study a second order differential operator with mixed nonlocal boundary conditions combined weighting integral boundary condition with another two point boundary condition. Under certain conditions on the weighting functions and on the coefficients in the boundary conditions, called non regular boundary conditions, we prove that the resolvent decreases with respect to the spec...

Abstract We study the Stokes problem for incompressible fluid with mixed nonlinear boundary conditions of subdifferential type. The latter involve a unilateral condition, Navier slip nonmonotone version Navier–Fujita and threshold leak condition frictional weak form leads to new class variational–hemivariational inequalities on convex sets velocity field. Solution existence compactness solution...

In this short note, we study the local well-posedness of a 3D model for incompressible Navier-Stokes equations with partical viscosity. This model was originally proposed by Hou-Lei in [4]. In a recent paper, we prove that this 3D model with partial viscosity will develop a finite time singularity for a class of initial condition using a mixed Dirichlet Robin boundary condition. The local well-...

We provide a polynomial decay rate for the energy of the wave equation with a dissipative boundary condition in a cylindrical trapped domain. A new kind of interpolation estimate for the wave equation with mixed Dirichlet-Neumann boundary condition is established from a construction based on a Fourier integral operator involving a good choice of weight functions.

Boundary critical phenomena are studied in the 3State Potts model in 2 dimensions using conformal field theory, duality and renormalization group methods. A presumably complete set of boundary conditions is obtained using both fusion and orbifold methods. Besides the previously known free, fixed and mixed boundary conditions a new one is obtained. This illustrates the necessity of considering f...

We prove sharp convergence rates for a class of domain embedding methods for elliptic boundary value problems. The theory is established for Dirichlet, Neumann, and Robin boundary conditions, and is unified in a new formulation for mixed boundary condition. On the continuous level, the methods for these boundary value problems perform equally well.

We prove that if the given compact set K is convex then a minimizer of the functional I(v) = ∫ BR |∇v|dx + Per({v > 0}), 1 < p < ∞, over the set {v ∈ H 0 (BR)| v ≡ 1 on K ⊂ BR} has a convex support, and as a result all its level sets are convex as well. We derive the free boundary condition for the minimizers and prove that the free boundary is analytic and the minimizer is unique.