Zobrazeno 1 - 10
of 80
pro vyhledávání: '"Borthagaray, Juan Pablo"'
We develop a monotone, two-scale discretization for a class of integrodifferential operators of order $2s$, $s \in (0,1)$. We apply it to develop numerical schemes, and derive pointwise convergence rates, for linear and obstacle problems governed by
Externí odkaz:
http://arxiv.org/abs/2405.17652
We prove Besov boundary regularity for solutions of the homogeneous Dirichlet problem for fractional-order quasi-linear operators with variable coefficients on Lipschitz domains $\Omega$ of $\mathbb{R}^d$. Our estimates are consistent with the bounda
Externí odkaz:
http://arxiv.org/abs/2305.17818
This survey hinges on the interplay between regularity and approximation for linear and quasi-linear fractional elliptic problems on Lipschitz domains. For the linear Dirichlet integral Laplacian, after briefly recalling H\"older regularity and appli
Externí odkaz:
http://arxiv.org/abs/2212.14070
We propose a First-Order System Least Squares (FOSLS) method based on deep-learning for numerically solving second-order elliptic PDEs. The method we propose is capable of dealing with either variational and non-variational problems, and because of i
Externí odkaz:
http://arxiv.org/abs/2204.07227
We prove Besov regularity estimates for the solution of the Dirichlet problem involving the integral fractional Laplacian of order $s$ in bounded Lipschitz domains $\Omega$: \[ \begin{aligned} \|u\|_{\dot{B}^{s+r}_{2,\infty}(\Omega)} \le C \|f\|_{L^2
Externí odkaz:
http://arxiv.org/abs/2110.02801
We consider the homogeneous Dirichlet problem for the integral fractional Laplacian $(-\Delta)^s$. We prove optimal Sobolev regularity estimates in Lipschitz domains provided the solution is $C^s$ up to the boundary. We present the construction of gr
Externí odkaz:
http://arxiv.org/abs/2109.00451
We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy minimization, a
Externí odkaz:
http://arxiv.org/abs/2105.06079
We propose and analyze a robust BPX preconditioner for the integral fractional Laplacian on bounded Lipschitz domains. For either quasi-uniform grids or graded bisection grids, we show that the condition numbers of the resulting systems remain unifor
Externí odkaz:
http://arxiv.org/abs/2103.12891
Publikováno v:
IMA Journal of Numerical Analysis, 42(4), pp.3207-3240, 2022
In this paper we consider approximations of Neumann problems for the integral fractional Laplacian by continuous, piecewise linear finite elements. We analyze the weak formulation of such problems, including their well-posedness and asymptotic behavi
Externí odkaz:
http://arxiv.org/abs/2008.06129
Publikováno v:
SIAM Journal on Numerical Analysis, 59(4), pp. 1918-1947
The integral fractional Laplacian of order $s \in (0,1)$ is a nonlocal operator. It is known that solutions to the Dirichlet problem involving such an operator exhibit an algebraic boundary singularity regardless of the domain regularity. This, in tu
Externí odkaz:
http://arxiv.org/abs/2005.03786