Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (1)

Search Parameters:
Keywords = the nonlocal Monge–Ampère equations

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
19 pages, 388 KB  
Article
The Maximal Regularity of Nonlocal Parabolic Monge–Ampère Equations and Its Monotonicity in the Whole Space
by Xingyu Liu
Axioms 2025, 14(7), 491; https://doi.org/10.3390/axioms14070491 - 24 Jun 2025
Cited by 2 | Viewed by 831
Abstract
The Monge–Ampère operator, as a nonlinear operator embedded in parabolic differential equations, complicates the demonstration of maximal regularity for these equations. This research uses the Riesz fractional derivative to connect the Monge–Ampère operator with the fractional Laplacian operator. It is then possible to [...] Read more.
The Monge–Ampère operator, as a nonlinear operator embedded in parabolic differential equations, complicates the demonstration of maximal regularity for these equations. This research uses the Riesz fractional derivative to connect the Monge–Ampère operator with the fractional Laplacian operator. It is then possible to seek the maximal regularity of the parabolic Monge–Ampère equations by following an approach similar to that used for finding the maximal regularity of the parabolic fractional Laplacian operator. The maximal regularity of nonlocal parabolic Monge–Ampère equations guarantees the existence of solutions in the whole space. Based on these conditions, a modified sliding method, an enhancement of the moving planes method, is employed to establish the monotonicity property of the solutions for the nonlocal parabolic Monge–Ampère equations in the whole space. Full article
Show Figures

Figure 1

Back to TopTop