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math.AP2025
Stationary equation of the relativistic heat diffusion in transparent media having --data
Francesco Balducci, Sergio Segura de León
Our objective is to prove existence of a solution to the Dirichlet problem for an equation arising in the theory of radiation hydrodynamics to deal with the radiating energy in tra…
math.AP2025
Existence of solutions for laplacian problems with singular first order terms
Francesco Balducci
We prove existence of solutions to the following problem \begin{equation*} \begin{cases} -Δ_1 u +g(u)|Du|=h(u)f & \text{in ,} \\ u=0 & \text{on ,} \end{cases} \end{eq…
math.AP2024
Existence and regularity of solutions for the elliptic nonlinear transparent media equation
Francesco Balducci, Francescantonio Oliva, Francesco Petitta +1
In this paper we study existence and regularity of solutions to Dirichlet problems as $$ \begin{cases} - {\rm div}\left(|u|^m\frac{D u}{|D u|}\right) = f & \text{in}\;Ω,\\ \newline…