In this paper we study the regularity properties of certain maximal operators convolution type at endpoint \(p=1\), when acting on radial data. particular, for heat flow operator and Poisson operator, initial datum \(u_0 \in W^{1,1}(\mathbf{R}^d)\) is a function, show that associated function \(u^*\) weakly differentiable \[\|\nabla u^*\|_{L^1(\mathbf{R}^d)} \lesssim_d \|\nabla u_0\|_{L^1(\math...

The Hermite Radial Basis Functions (HRBF) Implicits reconstruct an implicit function which interpolates or approximates scattered multivariate Hermite data (i.e., unstructured points and their corresponding normals). Experiments suggest that HRBF Implicits allow the reconstruction of surfaces rich in details and behave better than previous related methods under coarse and/or nonuniform sampling...

In this paper‎, ‎we decide to select the best center nodes‎ ‎of radial basis functions by applying the Multiple Criteria Decision‎ ‎Making (MCDM) techniques‎. ‎Two methods based on radial basis‎ ‎functions to approximate the solution of partial differential‎ ‎equation by using collocation method are applied‎. ‎The first is based‎ ‎on the Kansa's approach‎, ‎and the second is based on the Hermit...