$G$-convergence of elliptic and parabolic operators depending on vector fields

Abstract

We consider sequences of elliptic and parabolic operators in divergence form and depending on a family of vector fields. We show compactness results with respect to G-convergence, or H-convergence, by means of the compensated compactness theory, in a setting in which the existence of affine functions is not always guaranteed, due to the nature of the family of vector fields.

References in corpus (3)

• $\Gamma$-convergence for functionals depending on vector fields. I. Integral representation and compactness
• Integral representation of local left--invariant functionals in Carnot groups
• $\Gamma$-convergence for functionals depending on vector fields. II. Convergence of minimizers

Cited by in corpus (1)

• $H$-compactness for nonlocal linear operators in fractional divergence form