Orazio Arena

On a singular parabolic equation related to axially symmetric heat potentials

SummaryAn initial value problem for the following singular parabolic differential equation

Bounds for the nonhomogeneous GASPT equation

u_{x\alpha } + \frac{{2v}}{x}u_x = u_t (2v > - 1)

Elliptic extensions in the disk with operators in divergence form

is studied in some suitable weighted Sobolev class. Such an equation is related to axially symmetric problems and also occurs in probability theory. Uniqueness, existence and representation theorems for the solution are proved and differentiability and regularity properties are investigated. The non-homogeneous equation is also considered.

Degenerate elliptic-parabolic equation

This paper discusses the null boundary controllability of two PDE’s, modeling a composite solid with different physical properties in each layer. Interface conditions are imposed.

A problem of boundary controllability for a plate

SummaryWeighted a priori bounds for the equation Δu+(μ/y)uy=f(μ>0), in the halfplane y>0, are proved. If p>1, 0<α+p−1<1+μ, u has bounded support and yµuy→0 (as y→0+), then the Lp norms of uαu and yα∥D2u∥ are bounded by the Lp norm of yαf. A boundary value problem in a rectangle is also studied in the appropriate weighted Sobolev class.

Boundary control of two PDEs separated by interface conditions

For any and arbitrary with compact support, it is proved that there exists a pair (L, ), with L second order uniformly elliptic operator and such that a.e. in .

On Some Boundary Control Problems

Let

Maximal Lp-regularity for a parabolic evolution equation related to an elliptic discontinuous operator

\varphi_0