The fractional Laplacian in R d, which we write as (− Δ) α/2 with α∈(0, 2), has multiple
equivalent characterizations. Moreover, in bounded domains, boundary conditions must be …

Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …

Minimizers of functionals of the type w ↦ ∫ Ω [ | D w | p - f w ] d x + ∫ R n ∫ R n | w ( x ) - w (
y ) | γ | x - y | n + s γ d x d y \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} …

The normal derivative lemma and surrounding issues - IOPscience This site uses cookies. By
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In this paper, we develop a direct method of moving planes for the fractional Laplacian.
Instead of using the conventional extension method introduced by Caffarelli and Silvestre …

This paper deals with the integral version of the Dirichlet homogeneous fractional Laplace
equation. For this problem weighted and fractional Sobolev a priori estimates are provided …

We propose an abstract framework for analyzing the convergence of least-squares methods
based on residual minimization when feasible solutions are neural networks. With the norm …

We introduce a new Neumann problem for the fractional Laplacian arising from a simple
probabilistic consideration, and we discuss the basic properties of this model. We can …

In this paper we survey some results on the Dirichlet problem \left{_u=g^Lu=f_inR^n\Ω^inΩ\
right. for nonlocal operators of the form Lu\left(x\right)=PVR^n\left{u\left(x\right) …

In this paper we prove the Pohozaev identity for the semilinear Dirichlet problem (-Δ)^ su= f
(u)(-Δ) su= f (u) in Ω, u\equiv0 Ω, u≡ 0 in\mathbb R^ n \ Ω R n\Ω. Here, s ∈ (0, 1) s∈(0, 1) …