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On the time fractional heat equation with obstacle
Carlo Alberini, Raffaela Capitanelli, Mirko D'Ovidio +1
We study a Caputo time fractional degenerate diffusion equation which we prove to be equivalent to the fractional parabolic obstacle problem, showing that its solution evolves for…
Liouville type theorems and regularity of solutions to degenerate or singular problems part II: odd solutions
Yannick Sire, Susanna Terracini, Stefano Vita
We consider a class of equations in divergence form with a singular/degenerate weight Under suit…
Liouville type theorems and regularity of solutions to degenerate or singular problems part I: even solutions
Yannick Sire, Susanna Terracini, Stefano Vita
We consider a class of equations in divergence form with a singular/degenerate weight $$-\mathrm{div}(|y|^a A(x,y)\nabla u)=|y|^a f(x,y)\; \quad\textrm{or} \ \textrm{div}(|y|^aF(x,…
A quantitative stability estimate for the fractional Faber-Krahn inequality
Lorenzo Brasco, Eleonora Cinti, Stefano Vita
We prove a quantitative version of the Faber-Krahn inequality for the first eigenvalue of the fractional Dirichlet-Laplacian of order s. This is done by using the so-called Caffare…