Top-level heading

Hypoellipticity and loss of derivatives

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 ...

Flussi in rocce diatomitiche

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...

Derivation of rod theories from three-dimensional nonlinear elasticity by Gamma-convergence

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...

Regularity of solutions of partial differential equations in Lorentz spaces

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...

Regularity for nonconvex variational problems

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...

Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion

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...

Risultati di esistenza e non esistenza per equazioni ellittiche con non linearit`a esponenziali e dati misura

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...

Problemi ellittici relativi ad equazioni di campo a massa nulla

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 Brezis-Nirenberg problem in spaces with constant curvature

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...

Conservation law with discontinuous coefficent

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...
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