The nonlinear p-Laplace diffusion p > 1 was considered in the Cohen-Grossberg neural network CGNN , and a new linear matrix inequalities LMI criterion is obtained, which ensures the equilibrium of CGNN is stochastically exponentially stable. Note that , if p 2, p-Laplace diffusion is just the conventional Laplace diffusion in many previous literatures. And it is worth mentioning that even if p ...

Ergodicity for local and nonlocal stochastic singular p-Laplace equations is proven, without restriction on the spatial dimension and for all p ∈ [1, 2). This generalizes previous results from [Gess, Tölle; JMPA, 2014], [Liu, Tölle; ECP, 2011], [Liu; JEE, 2009]. In particular, the results include the multivalued case of the stochastic (nonlocal) total variation flow, which solves an open proble...

We present two methods for solving the electrostatics of point charges and multipoles on the surface of a sphere, i.e., in the space S2, with applications to numerical simulations of two-dimensional (2D) polar fluids. In the first approach, point charges are associated with uniform neutralizing backgrounds to form neutral pseudo-charges, while in the second, one instead considers bi-charges, i....

Conformally Stäckel manifolds can be characterized as the class of $n$-dimensional pseudo-Riemannian $(M,G)$ on which Hamilton–Jacobi equation $$ G(\nabla u, \nabla u) = 0 for null geodesics and Laplace $-\Delta\_G , \psi 0$ are solvable by R-separation variables. In particular case in metric has Riemannian signature, they provide explicit examples metrics admitting a set $n-1$ commuting confor...

We introduce stochastic Discrete Laplacian Growth and consider its deterministic continuous version. These are reminiscent respectively to well-known Diffusion Limited Aggregation and Hele-Shaw free boundary problem for the interface propagation. We study correlation between stability of deterministic free-boundary problem and macroscopic fractal growth in the corresponding discrete problem. It...

We relate the fractional powers of the discrete Laplacian with a standard time-fractional derivative in the sense of Liouville by encoding the iterative nature of the discrete operator through a time-fractional memory term.

When quantum fields are studied on manifolds with boundary, the corresponding one-loop quantum theory for bosonic gauge fields with linear covariant gauges needs the assignment of suitable boundary conditions for elliptic differential operators of Laplace type. There are however deep reasons to modify such a scheme and allow for pseudo-differential boundary-value problems. When the boundary ope...