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14 papers · 2 filters
Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
We compare several notion of weak (modulus of) gradient in metric measure spaces. Using tools from optimal transportation theory we prove density in energy of Lipschitz maps indepe…
Nonlocal phase-field systems with general potentials
Maurizio Grasselli, Giulio Schimperna
We consider a phase-field model where the internal energy depends on the order parameter in a nonlocal way. Therefore, the resulting system consists of the energy balance equation…
Improved interpolation inequalities, relative entropy and fast diffusion equations
Jean Dolbeault, Giuseppe Toscani
We consider a family of Gagliardo-Nirenberg-Sobolev interpolation inequalities which interpolate between Sobolev's inequality and the logarithmic Sobolev inequality, with optimal c…
Shape flows for spectral optimization problems
Dorin Bucur, Giuseppe Buttazzo, Ulisse Stefanelli
We consider a general formulation of gradient flow evolution for problems whose natural framework is the one of metric spaces. The applications we deal with are concerned with the…
Asymptotic uniform boundedness of energy solutions to the Penrose-Fife model
Giulio Schimperna, Antonio Segatti, Sergey Zelik
We study a Penrose-Fife phase transition model coupled with homogeneous Neumann boundary conditions. Improving previous results, we show that the initial value problem for this mod…
Global existence for a hydrogen storage model with full energy balance
Elena Bonetti, Pierluigi Colli, Philippe Laurençot
A thermo-mechanical model describing hydrogen storage by use of metal hydrides has been recently proposed in a paper by Bonetti, Frémond and Lexcellent. It describes the formation…