Virginia De Cicco

Harnack inequalities for fuchsian type weighted elliptic equations

Harnack type inequalities for nonnegative (weak) solutions of degenerate elliptic equations, in divergence form, are established. The asymptotic behavior of solutions of Fuchsian type weighted elliptic operators is also investigated.

Kinetic Formulation and Uniqueness for Scalar Conservation Laws with Discontinuous Flux

We prove a uniqueness result for BV solutions of scalar conservation laws with discontinuous flux in several space dimensions. The proof is based on the notion of kinetic solution and on a careful analysis of the entropy dissipation along the discontinuities of the flux.

Structure of Solutions of Multidimensional Conservation Laws with Discontinuous Flux and Applications to Uniqueness

We investigate the structure of solutions of conservation laws with discontinuous flux under quite general assumption on the flux. We show that any entropy solution admits traces on the discontinuity set of the coefficients and we use this to prove the validity of a generalized Kato inequality for any pair of solutions. Applications to uniqueness of solutions are then given.

A Chain Rule Formula in the Space BV and Applications to Conservation Laws

In this paper we prove a new chain rule formula for the distributional derivative of the composite function

A nonautonomous chain rule in W1,p and BV

v(x)=B(x,u(x))

Weak lower semicontinuity for non coercive polyconvex integrals

, where

Lower semicontinuity for nonautonomous surface integrals

u:\mathopen]a,b\mathclose[\to\mathbb{R}^d

On the chain rule formulas for divergences and applications to conservation laws

has bounded variation,

Lower Semicontinuity in SBV for Integrals with Variable Growth

B(x,\cdot)

An extension of the pairing theory between divergence-measure fields and BV functions

is continuously differentiable, and