P. Stinga

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20122022

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math.AP2022

Fractional derivatives: Fourier, elephants, memory effects, viscoelastic materials and anomalous diffusions

P. R. Stinga

This paper, that will appear in the Notices of the AMS, begins with a brief historical account of the beginnings of fractional calculus and the crucial roles played by Leibniz and…

math.AP2019

Regularity estimates for nonlocal space-time master equations in bounded domains

A. Biswas, P. R. Stinga

We obtain sharp parabolic interior and global Schauder estimates for solutions to nonlocal space-time master equations $(\partial_{t} + L)^{s} u = f$ in $R \times Ω$ , where $L$ …

math.AP2018

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

P. R. Stinga

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 r…

math.AP2018

Hölder, Sobolev, weak-type and $B M O$ estimates in mixed-norm with weights for parabolic equations

P. R. Stinga, J. L. Torrea

We prove weighted mixed-norm $L_{t}^{q} (W_{x}^{2, p})$ and $L_{t}^{q} (C_{x}^{2, α})$ estimates for $1 < p, q < \infty$ and $0 < α < 1$ , weighted mixed weak-type estimates for $q = 1$ , $L^\infty_{t}(L^p_x)-…

math.AP2018

Harnack inequalities and Hölder estimates for master equations

A. Biswas, M. De León-Contreras, P. R. Stinga

We study master equations of the form $(\partial_{t} + L)^{s} u = f in R \times Ω$ where $L$ is a divergence form elliptic operator and $Ω \subseteq R^{n}$ . These a…

math.AP2012

Extension problem and fractional operators: semigroups and wave equations

J. E. Galé, P. J. Miana, P. R. Stinga

We extend results of Caffarelli--Silvestre and Stinga--Torrea regarding a characterization of fractional powers of differential operators via an extension problem. Our results appl…

Fractional derivatives: Fourier, elephants, memory effects, viscoelastic materials and anomalous diffusions

Regularity estimates for nonlocal space-time master equations in bounded domains

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

Hölder, Sobolev, weak-type and BMO estimates in mixed-norm with weights for parabolic equations

Harnack inequalities and Hölder estimates for master equations

Extension problem and fractional operators: semigroups and wave equations

Hölder, Sobolev, weak-type and $B M O$ estimates in mixed-norm with weights for parabolic equations