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- W3119568384 abstract "We investigate regularity and a priori estimates for Fokker-Planck and Hamilton-Jacobi equations with unbounded ingredients driven by the fractional Laplacian of order $sin(1/2,1)$. As for Fokker-Planck equations, we establish integrability estimates under a fractional version of the Aronson-Serrin interpolated condition on the velocity field and Bessel regularity when the drift has low Lebesgue integrability with respect to the solution itself. Using these estimates, through the Evans' nonlinear adjoint method we prove new integral, sup-norm and Holder estimates for weak and strong solutions to fractional Hamilton-Jacobi equations with unbounded right-hand side and polynomial growth in the gradient. Finally, by means of these latter results, exploiting Calderon-Zygmund-type regularity for linear nonlocal PDEs and fractional Gagliardo-Nirenberg inequalities, we deduce optimal $L^q$-regularity for fractional Hamilton-Jacobi equations." @default.
- W3119568384 created "2021-01-18" @default.
- W3119568384 creator A5061642612 @default.
- W3119568384 date "2021-01-03" @default.
- W3119568384 modified "2023-09-27" @default.
- W3119568384 title "Transport equations with nonlocal diffusion and applications to Hamilton-Jacobi equations" @default.
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