A chain rule formula in BV and applications to conservation laws

In this paper we prove a new chain rule formula for the distributional derivative of the composite function $v(x)=B(x,u(x))$, where $u:]a,b[\to\R^d$ has bounded variation, $B(x,\cdot)$ is continuously differentiable and $B(\cdot,u)$ has bounded variation. We propose an application of this formula in order to deal in an intrinsic way with the discontinuous flux appearing in conservation laws in one space variable.Comment: 26 page

Anzellotti's pairing theory and the Gauss--Green theorem

In this paper we obtain a very general Gauss-Green formula for weakly differentiable functions and sets of finite perimeter. This result is obtained by revisiting Anzellotti's pairing theory and by characterizing the measure pairing $(\boldsymbol{A}, Du)$ when $\boldsymbol{A}$ is a bounded divergence measure vector field and $u$ is a bounded function of bounded variation.Comment: 27 page

Genetic Studies of Hydrogen Bacteria and Their Applications to Biological Life Support Systems Status Report No. 3, May 1 - Oct. 31, 1966

Genetic cultural stabilities of hydrogen bacteria for application to biological life support system

Lower semicontinuity for non autonomous surface integrals

Some lower semicontinuity results are established for nonautonomous surface integrals depending in a discontinuous way on the spatial variable. The proof of the semicontinuity results is based on some suitable approximations from below with appropriate functionals

Nonautonomous chain rules in BV with Lipschitz dependence

The aim of this paper is to state a nonautonomous chain rule in BV with Lipschitz dependence, i.e. a formula for the distributional derivative of the composite function v(x)=B(x,u(x)), where $u:R^N oR$ is a scalar function of bounded variation, $B(cdot,t)$ has bounded variation and $B(x,cdot)$ is only a Lipschitz continuous function. We present a survey of recent developments on the nonautonomous chain rules in BV. Formulas of this type are an useful tool especially in view to applications to lower semicontinuity for integral functional (see cite{DC,dcfv,DCFV2,dcl}) and to the conservation laws with discontinuous flux (see cite{CD,CDD,CDDG})

Observaciones sobre el proceso de conservación del cuerpo de la momia del Nevado del Chuscha

Fil: De Cicco, Carlos G.. Universidad Nacional de Cuy