37 citations · 157 across the 16 of their papers we have counts for
16 papers
On the divergence of the composition of irregular fields with BV functions
Graziano Crasta, Virginia De Cicco, Annalisa Malusa
We introduce a family of (nonlinear) pairing measures that ensure the validity of the divergence rule for composite functions , where $\boldsymbol{B}(\cdot,…
Relaxation for a degenerate functional with linear growth in the onedimensional case
Valeria Chiadò Piat, Virginia De Cicco, Anderson Melchor Hernandez
In this work, we study the relaxation of a degenerate functional with linear growth, depending on a weight that does not exhibit doubling or Muckenhoupt-type conditions. In ord…
Relaxation for degenerate nonlinear functionals in the onedimensional case
Valeria Chiadò Piat, Virginia De Cicco, Anderson Melchor Hernandez
In this study, we approach the analysis of a degenerate nonlinear functional in one dimension, accommodating a degenerate weight . Our investigation focuses on establishing an e…
Beyond : new pairings and Gauss-Green formulas for measure fields with divergence measure
Giovanni Eugenio Comi, Virginia De Cicco, Giovanni Scilla
A new notion of pairing between measure vector fields with divergence measure and scalar functions, which are not required to be weakly differentiable, is introduced. In particular…
Representation formulas for pairings between divergence-measure fields and functions
Giovanni E. Comi, Graziano Crasta, Virginia De Cicco +1
The purpose of this paper is to find pointwise representation formulas for the density of the pairing between divergence-measure fields and BV functions, in this way continuing the…
On the variational nature of the Anzellotti pairing
Graziano Crasta, Virginia De Cicco
In this paper we prove that the Anzellotti pairing can be regarded as a relaxed functional with respect to the weak* convergence in the space BV of functions of bounded variation.…
Lower semicontinuity in for nonautonomous surface integrals
Virginia De Cicco, Giovanni Scilla
We provide a sufficient condition for lower semicontinuity of nonautonomous noncoercive surface energies defined on the space of functions, whose dependence on the -var…
Pairings between bounded divergence-measure vector fields and BV functions
Graziano Crasta, Virginia De Cicco, Annalisa Malusa
We introduce a family of pairings between a bounded divergence-measure vector field and a function of bounded variation, depending on the choice of the pointwise representative…
An extension of the pairing theory between divergence-measure fields and BV functions
Graziano Crasta, Virginia De Cicco
In this paper we introduce a nonlinear version of the notion of Anzellotti's pairing between divergence--measure vector fields and functions of bounded variation, motivated by poss…
The Dirichlet problem for singular elliptic equations with general nonlinearities
Virginia De Cicco, Daniela Giachetti, Francescantonio Oliva +1
In this paper, under very general assumptions, we prove existence and regularity of distributional solutions to homogeneous Dirichlet problems of the form $$\begin{cases} \displays…
Anzellotti's pairing theory and the Gauss--Green theorem
Graziano Crasta, Virginia De Cicco
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 pair…
On the chain rule formulas for divergences and applications to conservation laws
Graziano Crasta, Virginia De Cicco
In this paper we prove a nonautonomous chain rule formula for the distributional divergence of the composite function , where $\boldsymbol…
A nonautonomous chain rule in and
Luigi Ambrosio, Graziano Crasta, Virginia De Cicco +1
In this paper we consider the chain rule formula for compositions in the case when has a Sobolev or BV regularity and is separately Sobolev, or B…
Structure of solutions of multidimensional conservation laws with discontinuous flux and applications to uniqueness
Graziano Crasta, Virginia De Cicco, Guido De Philippis +1
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 o…
Kinetic formulation and uniqueness for scalar conservation laws with discontinuous flux
Graziano Crasta, Virginia De Cicco, Guido De Philippis
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…
A chain rule formula in BV and applications to conservation laws
Graziano Crasta, Virginia De Cicco
In this paper we prove a new chain rule formula for the distributional derivative of the composite function , where has bounded variation, $B(x,\cd…