Results 11 to 20 of about 12,503,673 (230)

The Fractional Powers of the Sub-Laplacian in Carnot Groups Through an Analytic Continuation [PDF]

Journal of Geometric Analysis, 2023
In this paper we construct the fractional powers of the sub-Laplacian in Carnot groups through an analytic continuation approach. In addition, we characterize the powers of the fractional sub-Laplacian in the Heisenberg group, and as a byproduct we ...
Francesca Corni, Fausto Ferrari
semanticscholar   +1 more source

Alt–Caffarelli–Friedman monotonicity formula and mean value properties in Carnot groups with applications [PDF]

Bollettino dell'Unione Matematica Italiana, 2023
In this paper, we provide a different approach to the Alt–Caffarelli–Friedman monotonicity formula, reducing the problem to test the monotone increasing behavior of the mean value of a function involving the gradient’s norm.
Fausto Ferrari, N. Forcillo
semanticscholar   +1 more source

Direct Assembly of Micrometer-Long Polymeric Cylinders in Water via Supramolecular Sticker Engineering. [PDF]

Macromol Rapid Commun
Engineering order at the nanoscale: Tailored design of PDI and TEG‐functionalized poly(N,N‐dimethylacrylamide) enables direct assembly of micrometer‐long nanocylinders in water. TEG prevents clustering, while the polymer chain length governs the morphology.
Berruée S, Guigner JM, Huin C, Calupitan JP, Bouteiller L, Sosa Vargas L, Rieger J.   +6 more
europepmc   +2 more sources

Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot groups of step two [PDF]

Calculus of Variations and Partial Differential Equations, 2023
We prove that nonnegative almost minimizers of the horizontal Bernoulli-type functional J(u,Ω):=∫Ω(|∇Gu(x)|2+χ{u>0}(x))dx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}
Fausto Ferrari, N. Forcillo, Enzo Maria Merlino   +2 more
semanticscholar   +1 more source

Identifying 1-rectifiable measures in Carnot groups

Analysis and Geometry in Metric Spaces, 2023
We continue to develop a program in geometric measure theory that seeks to identify how measures in a space interact with canonical families of sets in the space. In particular, extending a theorem of M. Badger and R.
Badger Matthew, Li Sean, Zimmerman Scott
doaj   +1 more source

Exceptional families of measures on Carnot groups

Analysis and Geometry in Metric Spaces, 2023
We study the families of measures on Carnot groups that have vanishing pp-module, which we call Mp{M}_{p}-exceptional families. We found necessary and sufficient Conditions for the family of intrinsic Lipschitz surfaces passing through a common point to ...
Franchi Bruno, Markina Irina
doaj   +1 more source

A note on monotonicity and Bochner formulas in Carnot groups [PDF]

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2022
In this note, we prove two monotonicity formulas for solutions of $\Delta _H f = c$ and $\Delta _H f - \partial _t f = c$ in Carnot groups. Such formulas involve the right-invariant carré du champ of a function and they are false for the left-invariant ...
N. Garofalo
semanticscholar   +1 more source

Mean value formulas for classical solutions to some degenerate elliptic equations in Carnot groups [PDF]

Discrete and Continuous Dynamical Systems. Series A, 2022
We prove surface and volume mean value formulas for classical solutions to uniformly elliptic equations in divergence form with Hölder continuous coefficients.
D. Pallara, S. Polidoro
semanticscholar   +1 more source

Higher order boundary Schauder estimates in Carnot groups [PDF]

Mathematische Annalen, 2022
In his seminal 1981 study D. Jerison showed the remarkable negative phenomenon that there exist, in general, no Schauder estimates near the characteristic boundary in the Heisenberg group Hn.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage ...
Agnid Banerjee, N. Garofalo, Isidro H. Munive   +2 more
semanticscholar   +1 more source

Sharp Hardy Identities and Inequalities on Carnot Groups

Advanced Nonlinear Studies, 2021
In this paper we establish general weighted Hardy identities for several subelliptic settings including Hardy identities on the Heisenberg group, Carnot groups with respect to a homogeneous gauge and Carnot–Carathéodory metric, general nilpotent groups ...
Flynn Joshua, Lam Nguyen, Lu Guozhen
doaj   +1 more source