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On the Fractional Regularity for an Elliptic Nonlinear Singular Drift Equation

Year: 2025

Type: article

Abstract: ABSTRACT We consider an elliptic equation with the fractional Laplacian operator in the dissipative term, a singular integral operator in the nonlinear term, and an external source . The key example is the stationary (time‐independent) counterpart of the surface quasi‐geostrophic equation. Under suitable assumptions on and natural assumptions on in the setting of Sobolev spaces, our main result examines how the fractional power propagates and optimally improves the regularity of weak ‐solutions to this equation.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.70407

Author: Oscar Jarrín

Institution: Universidad de Las Américas

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4417424217

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Cites: 22

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