arXiv subjects
Publications and source records attributed to Jose A. Barrionuevo.
We prove L2 x L2 to weak L1 estimates for some novel bilinear maximal operators of Kakeya and lacunary type thus extending to this setting, the works of Cordoba and of Nagel, Stein and Wainger.
We derive general bounds for the large time size of supnorm values of solutions to one-dimensional advection-diffusion equations with initial data in Lp0 (R) \cap L1 for some 1 <= p0 < \infty, and arbitrary bounded advection speeds b(x, t), introducing techniques based on suitable energy arguments. Some open problems and related results are also given.
Using variants of the TT* method we give a self-contained proof of the result of Alfonseca, Soria and Vargas on maximal operators on arbitrary directions in $\rr^2$. We also give a sharp $L^2$ estimate for a maximal function extending a Theorem of Cordoba.
We obtain sufficient conditions for the stability of the synchronized solutions for a class of coupled dynamical systems. This is accomplished by finding an analytical expression for the transverse Liapunov exponent through spectral analysis. We then indicate some applications to population dynamics.