Simona Fornaro

Gradient estimates for parabolic problems with unbounded coefficients in non convex unbounded domains

Abstract We consider a class of uniformly elliptic operators 𝒜 with unbounded coefficients in unbounded domains . Under suitable assumptions on the geometry of and on the coefficients, we prove that the Cauchy-Neumann problem associated with the operator 𝒜 admits a unique bounded classical solution u for any initial datum f which is bounded and continuous in . Moreover, we prove uniform and pointwise gradient estimates for u. Finally, we give some applications of the so obtained estimates.

Elliptic operators with unbounded diffusion coefficients perturbed by inverse square potentials in

In this paper we give sufficient conditions on

L^p

\alpha \ge 0

--spaces

and

Measure valued solutions of sub-linear diffusion equations with a drift term

c\in R

L p -maximal regularity for non-autonomous evolution equations

ensuring that the space of test functions

Gradient estimates in parabolic problems with unbounded coefficients

C_c^\infty(R^N)

Gradient estimates for Dirichlet parabolic problems in unbounded domains

is a core for the operator \begin{eqnarray} L_0u=(1+|x|^\alpha )\Delta u+\frac{c}{|x|^2}u=:Lu+\frac{c}{|x|^2}u, \end{eqnarray} and

Intrinsic Harnack estimates for some doubly nonlinear degenerate parabolic equations

L_0

Lp-theory for some elliptic and parabolic problems with first order degeneracy at the boundary

with a suitable domain generates a quasi-contractive and positivity preserving