Author pages are created from data sourced from our academic publisher partnerships and public sources.

Publications Influence

Share This Author

Extension Problem and Harnack's Inequality for Some Fractional Operators

The fractional Laplacian can be obtained as a Dirichlet-to-Neumann map via an extension problem to the upper half space. In this paper we prove the same type of characterization for the fractional… Expand

Regularity Theory and Extension Problem for Fractional Nonlocal Parabolic Equations and the Master Equation

TLDR

Fractional elliptic equations, Caccioppoli estimates and regularity

- L. Caffarelli, P. Stinga
- Mathematics
- 26 September 2014

Let $L=-\operatorname{div}_x(A(x)\nabla_x)$ be a uniformly elliptic operator in divergence form in a bounded domain $\Omega$. We consider the fractional nonlocal equations $$\begin{cases}… Expand

Extension problem and fractional operators: semigroups and wave equations

- J. Galé, Pedro J. Miana, P. Stinga
- Mathematics
- 31 July 2012

We extend results of Caffarelli–Silvestre and Stinga–Torrea regarding a characterization of fractional powers of differential operators via an extension problem. Our results apply to generators of… Expand

Maximum principles, extension problem and inversion for nonlocal one-sided equations

- A. Bernardis, F. J. Mart'in-Reyes, P. Stinga, J. Torrea
- Mathematics
- 12 May 2015

We study one-sided nonlocal equations of the form $$\int_{x_0}^\infty\frac{u(x)-u(x_0)}{(x-x_0)^{1+\alpha}} dx=f(x_0),$$ on the real line. Notice that to compute this nonlocal operator of order… Expand

Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications

- 'Oscar Ciaurri, L. Roncal, P. Stinga, J. Torrea, J. L. Varona
- Mathematics
- 31 August 2016

The analysis of nonlocal discrete equations driven by fractional powers of the discrete Laplacian on a mesh of size $h>0$ \[ (-\Delta_h)^su=f, \] for $u,f:\mathbb{Z}_h\to\mathbb{R}$, $0<s<1$, is… Expand

User’s guide to the fractional Laplacian and the method of semigroups

- P. Stinga
- MathematicsFractional Differential Equations
- 15 August 2018

The \textit{method of semigroups} is a unifying, widely applicable, general technique to formulate and analyze fundamental aspects of fractional powers of operators $L$ and their regularity… Expand

Fractional semilinear Neumann problems arising from a fractional Keller–Segel model

- P. Stinga, B. Volzone
- Physics, Mathematics
- 28 June 2014

We consider the following fractional semilinear Neumann problem on a smooth bounded domain $$\Omega \subset \mathbb {R}^n$$Ω⊂Rn, $$n\ge 2$$n≥2, $$\begin{aligned} {\left\{ \begin{array}{ll}… Expand

Regularity estimates in Hölder spaces for Schrödinger operators via a $$T1$$ theorem

We derive Hölder regularity estimates for operators associated with a time-independent Schrödinger operator of the form $$-\Delta +V$$. The results are obtained by checking a certain condition on the… Expand

Fractional Laplacian on the torus

We study the fractional Laplacian $(-\Delta)^{\sigma/2}$ on the $n$-dimensional torus $\mathbb{T}^n$, $n\geq1$. First, we present a general extension problem that describes \textit{any} fractional… Expand

...

1

2

3

4

5

...