11 papers
Blow-up for a semilinear Tricomi equation in the oscillatory regime at the critical Strauss-type exponent
Diego Marcon, Wanderley Nunes do Nascimento, Matheus C. Santos
We study finite-time blow-up for a semilinear shifted Tricomi equation with decreasing propagation speed and an oscillatory scale-invariant mass. We focus on the Strauss-type criti…
Bernoulli problem for the fractional -Laplacian
Rafael Costa, Diego Marcon
We study regularity properties of minimizers for the one-phase Alt--Caffarelli problem associated with the fractional -Laplacian in the range . We consider minimizers of…
Gradient Regularity for Fully Nonlinear Equations with Variable Degeneracy and Hamiltonian Lower-Order Terms
Gleiciano Cosmo, Rafael R. Costa, Diego Marcon
We study local regularity properties of viscosity solutions to fully nonlinear elliptic equations with variable gradient degeneracy and Hamiltonian-type lower-order terms, \[ |\nab…
Blow-up for a Semilinear Tricomi-type Equation with Scale-Invariant Mass in the Oscillatory Regime
Diego Marcon, Wanderley Nascimento, Matheus Santos
We investigate the finite-time blow-up of solutions to a Tricomi-type equation with scale-invariant potential and power nonlinearities in the oscillatory regime. For smooth, compac…
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.…
Non-local diffusion with free boundaries
Diego Marcon, Rafayel Teymurazyan
We prove optimal regularity and derive several geometric properties for solutions of a free boundary problem with fractional diffusion. Additionally, we deduce local regu…
Homogenization of obstacle problems in Orlicz-Sobolev spaces
Diego Marcon, José Francisco Rodrigues, Rafayel Teymurazyan
We study the homogenization of obstacle problems in Orlicz-Sobolev spaces for a wide class of monotone operators (possibly degenerate or singular) of the -Laplacian type.…
The calculus of thermodynamical formalism
Paolo Giulietti, Benoit Kloeckner, Artur Lopes +1
Given a finite-to-one map acting on a compact metric space, one classically constructs for each potential in an appropriate Banach space of functionsa transfer operator acting on f…
On the Blow-up Criterion of Magnetohydrodynamics Equations in Homogeneous Sobolev Spaces
Diego Marcon, Wilberclay G. Melo, Lineia Schutz +1
In this paper, we obtain new lower bounds on the Homogeneous Sobolev--norms of the maximal solution of the Magnetohydrodynamics Equations. This gives us some insight on the blow-up…
A quantitative log-Sobolev inequality for a two parameter family of functions
Emanuel Indrei, Diego Marcon
We prove a sharp, dimension-free stability result for the classical logarithmic Sobolev inequality for a two parameter family of functions. Roughly speaking, our family consists of…