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Publications Influence

Extension Problem and Harnack's Inequality for Some Fractional Operators

- P. Stinga, J. L. Torrea
- Mathematics
- 14 October 2009

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

308 57- PDF

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

128 9- PDF

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

- P. Stinga, J. L. Torrea
- Computer Science, Mathematics
- SIAM J. Math. Anal.
- 5 November 2015

TLDR

42 8- PDF

Extension problem and fractional operators: semigroups and wave equations

- J. E. 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

46 5- PDF

Regularity properties of Schrödinger operators

- Tao Ma, P. Stinga, J. L. Torrea, C. Zhang
- Mathematics
- 4 July 2011

Abstract Let L be a Schrodinger operator of the form L = − Δ + V , where the nonnegative potential V satisfies a reverse Holder inequality. Using the method of L -harmonic extensions we study… Expand

22 4

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

62 3- PDF

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

26 3- PDF

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

- A. Bernardis, F. J. Martín-Reyes, P. Stinga, J. L. 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

32 3- PDF

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

- P. Stinga
- Mathematics
- 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

27 3- PDF

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

- 'O. Ciaurri, L. Roncal, P. Stinga, J. L. 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

27 2- PDF