We obtain boundary estimates for the gradient of solutions to elliptic systems with Dirichlet or Neumann boundary conditions and L1–data, under some condition on the divergence of the data. Similar boundary estimates are obtained for div–curl and Hodge systems. Mathematics Subject Classification (2000) 35J25 (26D15, 35F05)

We investigate sectoriality and maximal regularity in L-LSobolev spaces for the structurally damped plate equation with DirichletNeumann (clamped) boundary conditions. We obtain unique solutions with optimal regularity for the inhomogeneous problem in the whole space, in the half-space, and in bounded domains of class C. It turns out that the first-order system related to the scalar equation on...

In this paper, we extend the results obtained by Ruf–Srikanth [8]. We prove the existence of positive solution under Dirichlet and Neumann boundary conditions, which concentrate near the inner boundary and outer boundary respectively of an annulus as ε → 0. In fact, our result is independent of the dimension of RN .

In this work we show that, generically in the set of C2 bounded regions of Rn, n ≥ 2, the inequality R Ω φ 3 6= 0 holds for any eigenfunction of the Laplacian with either Dirichlet or Neumann boundary conditions.

A simple and short proof is given for the existence and uniqueness of the solution to the obstacle scattering problem under weak smoothness assumptions on the obstacle. The Robin, Neumann and Dirichlet boundary conditions are considered.

We consider the inverse boundary value problem in the case of discrete electrical networks containing nonlinear (non-ohmic) conductors. For a fixed nonlinear electrical network, we show that under reasonable assumptions, there are well-defined Dirichletto-Neumann and Neumann-to-Dirichlet maps relating boundary voltages and boundary currents. We also generalize work of Curtis, Morrow, and others...

We consider the continuum parabolic Anderson model (PAM) and dynamical Φ4 equation on 3-dimensional cube with boundary conditions. While Dirichlet solution theories are relatively standard, case of Neumann/Robin conditions gives rise to a divergent renormalisation. Furthermore for Φ34 ‘boundary triviality’ result is obtained: if one approximates Neumann usual bulk renormalisation, then limiting...

With a sufficiently fine discretisation, the Lattice Boltzmann Method (LBM) mimics second order Crank-Nicolson scheme for certain types of balance laws (Farag et al. [2021]). This allows explicit, highly parallelisable LBM to efficiently solve fundamental equations solid mechanics: conservation mass, linear momentum, and constitutive relations. To date, all algorithms simulation - see e.g. Murt...