Zobrazeno 1 - 10
of 76
pro vyhledávání: '"Torrea, J. L."'
First, we establish the theory of fractional powers of first order differential operators with zero order terms, obtaining PDE properties and analyzing the corresponding fractional Sobolev spaces. In particular, our study shows that Lebesgue and Sobo
Externí odkaz:
http://arxiv.org/abs/2205.00050
Our principal result is the following. Let $X$ and $Y$ be Banach spaces, let $G$ be a locally compact abelian group, and let $K$ be an operator valued kernel defined on $G$ with values in the space of bounded linear operators from $X$ to $Y$. Suppose
Externí odkaz:
http://arxiv.org/abs/2003.07906
Autor:
Stinga, P. R., Torrea, J. L.
We prove weighted mixed-norm $L^q_t(W^{2,p}_x)$ and $L^q_t(C^{2,\alpha}_x)$ estimates for $1
Externí odkaz:
http://arxiv.org/abs/1808.01311
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
Externí odkaz:
http://arxiv.org/abs/1608.08913
Novel global weighted parabolic Sobolev estimates, weighted mixed-norm estimates and a.e. convergence results of singular integrals for evolution equations are obtained. Our results include the classical heat equation, the harmonic oscillator evoluti
Externí odkaz:
http://arxiv.org/abs/1602.00757
Autor:
Stinga, P. R., Torrea, J. L.
We develop the regularity theory for solutions to space-time nonlocal equations driven by fractional powers of the heat operator $$(\partial_t-\Delta)^su(t,x)=f(t,x),\quad\hbox{for}~0
Externí odkaz:
http://arxiv.org/abs/1511.01945
We define and study some properties of the fractional powers of the discrete Laplacian $$(-\Delta_h)^s,\quad\hbox{on}~\mathbb{Z}_h = h\mathbb{Z},$$ for $h>0$ and $0
Externí odkaz:
http://arxiv.org/abs/1507.04986
We study one-sided nonlocal equations of the form $$\int_{x_0}^\infty\frac{u(x)-u(x_0)}{(x-x_0)^{1+\alpha}} dx=f(x_0),$$ on the real line. Notice that to compute this nonlocal operator of order $0<\alpha<1$ at a point $x_0$ we need to know the values
Externí odkaz:
http://arxiv.org/abs/1505.03075
It is well-known that the fundamental solution of $$ u_t(n,t)= u(n+1,t)-2u(n,t)+u(n-1,t), \quad n\in\mathbb{Z}, $$ with $u(n,0) =\delta_{nm}$ for every fixed $m \in\mathbb{Z}$, is given by $u(n,t) = e^{-2t}I_{n-m}(2t)$, where $I_k(t)$ is the Bessel f
Externí odkaz:
http://arxiv.org/abs/1401.2091
The weighted Lebesgue spaces of initial data for which almost everywhere convergence of the heat equation holds was only very recently characterized. In this note we show that the same weighted space of initial data is optimal for the heat--diffusion
Externí odkaz:
http://arxiv.org/abs/1206.4530