4 papers
Quantitative Osgood regularity for DiPerna--Lions flows
Henrique Borrin, João Fernando Nariyoshi
We study the spatial regularity of regular Lagrangian flows associated with vector fields in the DiPerna--Lions class \(\boldsymbol b\in L^1((0,T);W^{1,1}_{\loc}(\mathbb R^d)), \)…
Quantitative estimates for flows of regular Lagrangian flows for Hörmander singular kernels and LD vector fields
Henrique Borrin
In this paper, we obtain quantitative estimates of regular Lagrangian flows associated to vector fields whose derivative can be written as convolution of a fundamental singular ker…
An obstacle problem arising from American options pricing: regularity of solutions
Henrique Borrin, Diego Marcon
We analyse the obstacle problem for the nonlocal parabolic operator \[\partial_t u + (-Δ)^{s} u - b \cdot \nabla u - \mathcal{I}u - ru,\] where , …
On the Lagrangian structure of transport equations: relativistic Vlasov systems
Henrique Borrin, Diego Marcon
We study the Lagrangian structure of relativistic Vlasov systems, such as the relativistic Vlasov-Poisson and the relativistic quasi-eletrostatic limit of Vlasov-Maxwell equations.…