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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
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 $$\begin{cases}… Expand
Regularity Theory and Extension Problem for Fractional Nonlocal Parabolic Equations and the Master Equation
- P. Stinga, J. L. Torrea
- Computer Science, Mathematics
- SIAM J. Math. Anal.
- 5 November 2015
TLDR
Extension problem and fractional operators: semigroups and wave equations
- J. E. Galé, Pedro J. Miana, P. Stinga
- Mathematics
- 31 July 2012
We extend results of Caffarelli–Silvestre and Stinga–Torrea regarding a characterization of fractional powers of differential operators via an extension problem. Our results apply to generators of… Expand
Regularity properties of Schrödinger operators
- Tao Ma, P. Stinga, J. L. Torrea, C. Zhang
- Mathematics
- 4 July 2011
Abstract Let L be a Schrodinger operator of the form L = − Δ + V , where the nonnegative potential V satisfies a reverse Holder inequality. Using the method of L -harmonic extensions we study… Expand
Fractional Laplacian on the torus
We study the fractional Laplacian $(-\Delta)^{\sigma/2}$ on the $n$-dimensional torus $\mathbb{T}^n$, $n\geq1$. First, we present a general extension problem that describes \textit{any} fractional… Expand
Fractional semilinear Neumann problems arising from a fractional Keller–Segel model
- P. Stinga, B. Volzone
- Physics, Mathematics
- 28 June 2014
We consider the following fractional semilinear Neumann problem on a smooth bounded domain $$\Omega \subset \mathbb {R}^n$$Ω⊂Rn, $$n\ge 2$$n≥2, $$\begin{aligned} {\left\{ \begin{array}{ll}… Expand
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
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
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