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In this paper, we study a semilinear system involving the curl operator in a bounded and convex domain in $R^3$, which comes from the steady-state approximation for Bean critical-state model for type-II superconductors. We show the existence and the $L^{infty}$ estimate for weak solutions to this system.
We study the following nonlinear critical curl-curl equation begin{equation}label{eq0.1} ablatimes ablatimes U +V(x)U=|U|^{p-2}U+ |U|^4U,quad xin mathbb{R}^3,end{equation} where $V(x)=V(r, x_3)$ with $r=sqrt{x_1^2+x_2^2}$ is 1-periodic in $x_3$ dire
We present a novel approach to adjust global image properties such as colour, saturation, and luminance using human-interpretable image enhancement curves, inspired by the Photoshop curves tool. Our method, dubbed neural CURve Layers (CURL), is desig
This paper deals with a boundary-value problem in three-dimensional smooth bounded convex domains for the coupled chemotaxis-Stokes system with slow $p$-Laplacian diffusion begin{equation} onumber left{ begin{aligned} &n_t+ucdot abla n= ablacdo
In this paper, we establish a global regularity result for the optimal transport problem with the quadratic cost, where the domains may not be convex. This result is obtained by a perturbation argument, using a recent global regularity of optimal transportation in convex domains by the authors.
Edge (or Nedelec) finite elements are theoretically sound and widely used by the computational electromagnetics community. However, its implementation, specially for high order methods, is not trivial, since it involves many technicalities that are n