27 citations · 173 across the 52 of their papers we have counts for
6 papers · 1 filter
Nonlocal diffusion equations with dynamical boundary conditions
Pablo M. Berna, Julio D. Rossi
In this paper we study nonlocal problems that are analogous to the local ones given by the Laplacian or the p-Laplacian with dynamical boundary conditions. We deal both with smooth…
A Convection-Diffusion model on a star shaped graph
Cristian M. Cazacu, Liviu I. Ignat, Ademir F. Pazoto +1
In this paper we study a convection-diffusion equation on a star-shaped graph composed by incoming edges and outgoing edges with a nonlinearity $f\in C^1(\rr)$ satisfying s…
Convex envelopes on Trees
Leandro M. Del Pezzo, Nicolas Frevenza, Julio D. Rossi
We introduce two notions of convexity for an infinite regular tree. For these two notions we show that given a continuous boundary datum there exists a unique convex envelope on th…
Coupling local and nonlocal evolution equations
Alejandro Gárriz, Fernando Quirós, Julio D. Rossi
We prove existence, uniqueness and several qualitative properties for evolution equations that combine local and nonlocal diffusion operators acting in different subdomains and cou…
Dirichlet-to-Neumann maps on Trees
Leandro M. Del Pezzo, Nicolás Frevenza, Julio D. Rossi
In this paper we study the Dirichlet-to-Neumann map for solutions to mean value formulas on trees. We give two alternative definition of the Dirichlet-to-Neumann map. For the first…
The evolution problem associated with eigenvalues of the Hessian
Pablo Blanc, Carlos Esteve, Julio D. Rossi
In this paper we study the evolution problem \[ \left\lbrace\begin{array}{ll} u_t (x,t)- λ_j(D^2 u(x,t)) = 0, & \text{in } Ω\times (0,+\infty), \\ u(x,t) = g(x,t), & \text{on } \pa…