We investigate the limiting behavior of solutions to inhomogeneous $p$-Laplacian equation $-\Delta_p u = \mu_p$ subject Neumann boundary conditions. For right hand sides which are arbitrary signed measures we show that converge a Kantorovich potential associated with geodesic Wasserstein-$1$ distance. In regular case continuous characterize limit as viscosity solution an infinity Laplacian / ei...

In this paper, the multigrid algorithm was used to solve Poisson’s equation for various right-hand sides. However, in order to calculate the discretized laplacian value, both a second-order and a fourth-order laplacian operator was used. The fourth-order laplacian operator achieves higher accuracy at the cost of more calculations and a longer execution time. In order to compensate for this, the...

Ultrasound modulation of electrical or optical properties of materials offers the possibility to devise hybrid imaging techniques that combine the high electrical or optical contrast observed in many settings of interest with the high resolution of ultrasound. Mathematically, these modalities require that we reconstruct a diffusion coefficient σ(x) for x ∈ X, a bounded domain in Rn, from knowle...

We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.

In this paper we study decay properties of the solutions to the wave equation of p−Laplacian type with a weak nonlinear dissipative.

We perform an asymptotic analysis of models of population dynamics with a fractional Laplacian and local or nonlocal reaction terms. The first part of the paper is devoted to the long time/long range rescaling of the fractional Fisher-KPP equation. This rescaling is based on the exponential speed of propagation of the population. In particular we show that the only role of the fractional Laplac...

In this article, we study the oscillation of second order forced impulsive differential equation with γ-Laplacian and nonlinearities given by Riemann-Stieltjes integrals of the form