Corpus ID: 195316427

$H$-convergence for equations depending on monotone operators in Carnot groups

@article{Maione2019HconvergenceFE,
  title={\$H\$-convergence for equations depending on monotone operators in Carnot groups},
  author={Alberto Maione},
  journal={arXiv: Analysis of PDEs},
  year={2019}
}
Let $\Omega$ be an open and bounded subset of a Carnot Group $\mathbb{G}$ and $2\leq p<\infty$. In this paper we present some results related to the convergence of solutions of Dirichlet problems for sequences of monotone operators. The aim of this paper is to give a generalization of well-known results of Tartar, De Arcangelis-Serra Cassano and Baldi-Franchi-Tchou-Tesi in more general frameworks. 
3 Citations
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References

SHOWING 1-10 OF 39 REFERENCES
$\Gamma$-convergence for functionals depending on vector fields. II. Convergence of minimizers
Given a family of locally Lipschitz vector fieldsX(x) = (X1(x), . . . , Xm(x)) on R n, m ≤ n, we study integral functionals depending on X . Using the results in [MPSC1], we study the convergence ofExpand
G-convergence of monotone operators
Abstract A general notion of G-convergence for sequences of maximal monotone operators of the form is introduced in terms of the asymptotic behavior, as h → + ∞, of the solutions u h to the equationsExpand
On the convergence of solutions of degenerate elliptic equations in divergence form
SummaryIt is studied the convergence of solutions of Dirichlet problems for sequences of monotone operators of the type — div (ah (x, D·)), where the functions ah verify the following degenerateExpand
Asymptotic Behaviours in Fractional Orlicz–Sobolev Spaces on Carnot Groups
In this article, we define a class of fractional Orlicz–Sobolev spaces on Carnot groups, and in the spirit of the celebrated results of Bourgain–Brezis–Mironescu and of Maz’ya–Shaposhnikova, we studyExpand
Homogenization of monotone operators in divergence form with x-dependent multivalued graphs
In a previous paper [4], we proved the existence of solutions to −div a(x, grad u) = f , together with appropriate boundary conditions, whenever a(x, e) belongs, for every fixed x, to a certain classExpand
Compensated compactness for differential forms in Carnot groups and applications
Abstract In this paper we prove a compensated compactness theorem for differential forms of the intrinsic complex of a Carnot group. The proof relies on an L s -Hodge decomposition for these forms.Expand
Homogenization of almost periodic monotone operators
Abstract We determine some sufficient conditions for the G-convergence of sequences of quasi-linear monotone operators, together with an asymptotic formula for the G-limit. We then prove aExpand
div-curl Type Theorem, H-Convergence, and Stokes Formula in the Heisenberg Group
In this paper, we prove a div–curl type theorem in the Heisenberg group ℍ1, and then we develop a theory of H-convergence for second order differential operators in divergence form in ℍ1. TheExpand
Γ-convergence for functionals depending on vector fields. I. Integral representation and compactness
Abstract Given a family of locally Lipschitz vector fields X ( x ) = ( X 1 ( x ) , … , X m ( x ) ) on R n , m ≤ n , we study functionals depending on X. We prove an integral representation for localExpand
Stratified Lie groups and potential theory for their sub-Laplacians
The existence, for every sub-Laplacian, of a homogeneous fundamental solution smooth out of the origin, plays a crucial role in the book. This makes it possible to develop an exhaustive PotentialExpand
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