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We study existence questions and qualitative properties of solutions to variational problems related to minimization of geometric quantities, such as generalized notions of length of curves and of the area of surfaces, in a suitable sense. In the first part we consider a nonnegative multi-well po...
We study existence questions and qualitative properties of solutions to variational problems related to minimization of geometric quantities, such as generalized notions of length of curves and of the area of surfaces, in a suitable sense. In the first part we consider a nonnegative multi-well po...
We prove an inequality concerning isometries of a Gromov hyperbolic metric space, which does not require the space to be proper or geodesic. It involves the joint stable length, a hyperbolic version of the joint spectral radius, and shows that sets of isometries behave like sets of 2×2 real matri...
This Ph.D. thesis aims to obtain and to develop some mathematical models to understand some aspects of the dynamics of heterogeneous granular fluids. More precisely, the expected result is to develop three models, one where the dynamics of the granular material is modeled using a mixture theory a...
This thesis is dedicated to the study of the stationary Boussinesq system: u + (u r)u + r = g in , div u = 0 in , (0.1a) + u r = h in , (0.1b) where R3 is an open bounded connected set; u, and are the velocity field, pressure a
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