Work

$$C^{1,{1}/{3}-}$$ very weak solutions to the two dimensional Monge–Ampère equation

Year: 2025

Type: article

Abstract: For any $$\theta <\frac{1}{3}$$ θ < 1 3 , we show that very weak solutions to the two-dimensional Monge–Ampère equation with regularity $$C^{1,\theta }$$ C 1 , θ are dense in the space of continuous functions. This result is shown by a convex integration scheme involving a subtle decomposition of the defect at each stage. The decomposition diagonalizes the defect and, in addition, incorporates some of the leading-order error terms of the first perturbation, effectively reducing the required amount of perturbations to one.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-025-03019-0

Authors: Wentao Cao, Jonas Hirsch, Dominik Inauen

Institutions: Capital Normal University, Leipzig University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: National Natural Science Foundation of China, Universität Leipzig