We study hypoellopticity, in the sense of C∞ local hypoellipticity, which is defined as follows. If E is a partial differential operator on Rn, if P∈Rn, then E is hypoelliptic at P if whenever u is a ...
Rocce diatomitiche sono caratterizzate da bassa permeabilita e alta porosit `a. Si trovano per esempio in California, dove conten- gono petrolio di alta qualita. Da vari decenni gli ingegneri utalizza...
Using a variational approach we rigorously deduce some one-dimensional models for rods from three-dimensional nonlinear elasticity, passing to the limit as the diameter of the rod goes to zero. In par...
I look at improving the $L^p$ regularity results of Stampacchia for solutions of a scalar elliptic equation with discontinuous coefficients, by using my approach of Sobolev imbedding theorem in Lorent...
We discuss regularity and uniqueness questions for variational problems under minimal structural assumptions. The only assumption is that the integrand is close to the p-Dirichlet integrand at infinit...
Let $Ω$ be a bounded domain of class $C^2$ in $R^n$. If $u$ is a positive solution of $-∆u + u^q = 0$ in $Ω$ with $q > 1$ it admits a boundary trace $ν = Tr_{∂Ω}(u)$ in the class $B^+_{reg}(∂Ω)$ of...
Verra preso in esame il problema di Dirichlet omogeneo per l’equazione −∆u+exp(u)=µ posta in un dominio limitato di Rn, con n≥2, dove µ e` una misu- ra di Radon concentrata, nel caso modello, su un in...
Si cercano soluzioni di enegia finita per equazioni del tipo −∆u=f(u) ove u vive in un dominio illimitato di Rn ed f diverge al divergere del suo argomento. Si dice che un’equazione di questo tipo e` ...
The study of the Brezis-Nirenberg problem in domainson the sphere leads to new concentration phenomena which appear for small parameters. For domains in the hyperbolic space the situation is similar a...
Let f,g∈C1(R) and H be the Heaviside function. Consider the scalar conservation law ut+F(x,u)=0, u(x,0)=u0(x) for x∈R, t>0 and F(x,u)=H(x)f(u)+(1−H(x))g(u). Since the flux F is discontinuous at x...
