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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.AP2022
Regularity of viscosity solutions to fully nonlinear elliptic transmission problems
M. Soria-Carro, P. R. Stinga
We develop the regularity theory of viscosity solutions to transmission problems for fully nonlinear second order uniformly elliptic equations. Our results give a complete theory o…
math.CA2022
Fractional powers of first order differential operators and new families of polynomials associated to inverse measures
M. Mazzitelli, P. R. Stinga, J. L. Torrea
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…