- Adaptive finite issue approximations of the first eigenpair associated to p-Laplacian(arXiv)
Author : G. Li, J. Li, J. Merten, Y. Xu, S. Zhu
Abstract : On this paper, we recommend an adaptive finite issue methodology for computing the first eigenpair of the p-Laplacian draw back. We present that starting from a high-quality preliminary mesh our proposed adaptive algorithm produces a sequence of discrete first eigenvalues that converges to the first eigenvalue of the continuous draw back and the house between discrete eigenfunctions and the normalized eigenfunction set with respect to the first eigenvalue in W1,p-norm moreover tends to zero. In depth numerical examples are provided to level out the effectiveness and effectivity.
2. Good boundary regularity for the singular fractional p-Laplacian(arXiv)
Author : : Antonio Iannizzotto, Sunra Mosconi
Abstract : We analysis the boundary weighted regularity of weak choices u to a s-fractional p-Laplacian equation in a bounded clear space Ω with bounded response and nonlocal Dirichlet kind boundary state of affairs, inside the singular case p∈(1,2) and with s∈(0,1). We present that u/dsΩ has a α-Hölder regular extension to the closure of Ω, dΩ(x) which implies the house of x from the complement of Ω. This final result corresponds to that of ref. [28] for the degenerate case p≥2.
