Some recent results on the existence of global-in-time weak solutions to the Navier-Stokes equations of a general barotropic fluid
Some recent results on the Muskat problem
We consider the dynamics of an interface given by two incompressible fluids with different characteristics evolving by Darcy’s law. This scenario is known as the Muskat problem, being in 2D mathematically analogous to the two-phase Hele-Shaw cell. The purpose of this paper is to outline recent results on local existence, weak solutions, maximum principles and global existence.
Some regularity results for a family of variational inequalities
Some Regularity Results for Quasilinear Elliptic Systems of Second Order.
Some regularity results for quasi-linear parabolic systems
Some regularity results for quasilinear parabolic systems
Some regularity theorems in riemannian geometry
Some regularizing methods for transport equations and the regularity of solutions to scalar conservation laws
We study several regularizing methods, stationary phase or averaging lemmas for instance. Depending on the regularity assumptions that are made, we show that they can either be derived one from the other or that they lead to different results. Those are applied to Scalar Conservation Laws to precise and better explain the regularity of their solutions.
Some relatively new techniques for nonlinear problems.
Some remark on the nonexistence of positive solutions for some -Laplacian systems.
Some remarkable properties of -graphs.
Some remarks on a class of elliptic equations with degenerate coercivity
We study degenerate elliptic problems of the type
Some remarks on a result of Talenti
Some remarks on a second order evolution equation.
Some remarks on almost-positivity of 's
Per una classe di operatori pseudodifferenziali a caratteristiche multiple vengono date condizioni necessarie e sufficienti per la validità di stime dal basso «ottimali»
Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities.
Some remarks on bounded and unbounded weak solutions of elliptic systems.
Some remarks on conservative symmetric-hyperbolic systems governing relativistic theories
Some remarks on double-wells in one and three dimensions
Some remarks on eigenfunction expansions for Schrödinger operators with non-local potentials.